Journal of Mathematical Analysis and Applications最新文献

{"title":"Linear deformations of Heisenberg modules and Gabor frames","authors":"Malte Gerhold ,&nbsp;Arvin Lamando ,&nbsp;Franz Luef","doi":"10.1016/j.jmaa.2026.130540","DOIUrl":"10.1016/j.jmaa.2026.130540","url":null,"abstract":"<div><div>Heisenberg modules over noncommutative tori may also be viewed as Gabor frames. Building on this fact, we relate to deformations of noncommutative tori a bundle of Banach spaces induced by Heisenberg modules. The construction of this bundle of Banach spaces rests on deformation results of Gabor frames with windows in Feichtinger's algebra due to Feichtinger and Kaiblinger. We extend some of these results to Heisenberg modules, e.g. we establish an analog of the results by Feichtinger-Kaiblinger and a Balian-Low theorem. Finally, we extend our results to several generators on the bundle of Heisenberg modules and show that they provide a generalized Fell's condition on the bundle of noncommutative tori.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130540"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lie symmetry, power series solutions and conservation laws of a damped hyperbolic mean curvature flow","authors":"Tianao Zheng,&nbsp;Haoyu Xu,&nbsp;Zenggui Wang","doi":"10.1016/j.jmaa.2026.130507","DOIUrl":"10.1016/j.jmaa.2026.130507","url":null,"abstract":"<div><div>By means of Lie symmetry method, this paper constructs exact solutions of a damped hyperbolic mean curvature flow. The infinitesimal generators, commutative relation, and the optimal system for the damped hyperbolic flow are analysed. The power series solutions are constructed in terms of the power series method. Subsequently, the exact periodic solutions are constructed. Finally, Ibragimov's method is employed to obtain the conservation laws of the hyperbolic flow.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130507"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On certain maximality results involving products of possibly unbounded operators","authors":"Souheyb Dehimi ,&nbsp;Mohammed Hichem Mortad","doi":"10.1016/j.jmaa.2026.130513","DOIUrl":"10.1016/j.jmaa.2026.130513","url":null,"abstract":"<div><div>This paper is concerned with operator inclusions of the form <span><math><mi>T</mi><mo>⊆</mo><mi>A</mi><mi>B</mi></math></span>, where <em>A</em>, <em>B</em>, and <em>T</em> are linear operators, possibly unbounded and belonging to specific classes. The main objective is to establish conditions under which this inclusion becomes a full equality; that is, when <span><math><mi>T</mi><mo>=</mo><mi>A</mi><mi>B</mi></math></span> in the strong sense-meaning both the domains and the actions of the operators coincide. The results obtained extend a well-known theorem due to Devinatz, Nussbaum, and von Neumann.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130513"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Null controllability for a cascade system of backward stochastic semi-discrete fourth- and second-order parabolic equations","authors":"Yuan Lu,&nbsp;Liu Liu","doi":"10.1016/j.jmaa.2026.130466","DOIUrl":"10.1016/j.jmaa.2026.130466","url":null,"abstract":"<div><div>In this paper, we study the <em>ϕ</em>-null controllability property for a cascade system of coupled backward stochastic semi-discrete fourth- and second-order parabolic equations, where semi-discrete means that the spatial variable is discretized using a finite difference scheme, while the time variable remains continuous. Moreover, we get a relaxed observability estimate for the forward stochastic coupled equations by establishing a new discrete Carleman estimate, and further obtain the <em>ϕ</em>-null controllability of the cascade stochastic semi-discrete parabolic system via the classical duality arguments.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130466"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularity properties of distributions of correspondences without countable generation: applications to large games","authors":"Motoki Otsuka","doi":"10.1016/j.jmaa.2026.130539","DOIUrl":"10.1016/j.jmaa.2026.130539","url":null,"abstract":"<div><div>We show that each of the regularity properties of regular conditional distributions of correspondences—convexity, closedness, compactness, and preservation of closed graphs—is equivalent to the condition of nowhere equivalence. This result does not require any countable-generation assumptions. As an application, we establish the existence of a pure-strategy equilibrium for large games with general trait spaces. The trait space may be an arbitrary measurable space. As a corollary, we obtain the existence of a pure-strategy equilibrium in semi-anonymous settings in which payoffs depend, in addition to agents' own actions, on the joint distribution over the space of agents and actions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130539"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On differentiability and mass distributions of multivariate Archimedean copulas","authors":"Nicolas Pascal Dietrich,&nbsp;Wolfgang Trutschnig","doi":"10.1016/j.jmaa.2026.130523","DOIUrl":"10.1016/j.jmaa.2026.130523","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Copulas, in particular Archimedean copulas are commonly viewed as analytically nice and regular objects. Motivated by a recently established result stating that the first partial derivatives of bivariate copulas can exhibit surprisingly pathological behavior, we focus on the class of &lt;em&gt;d&lt;/em&gt;-dimensional Archimedean copulas denoted by &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; and show that partial derivatives of order &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; can be surprisingly irregular as well. In fact, we prove the existence of Archimedean copulas &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; whose &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-st order partial derivatives are pathological in the sense that for almost every &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; the derivative &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; does not exist on a dense set of &lt;span&gt;&lt;math&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Since the existence of mixed partial derivatives of order &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; of a copula &lt;em&gt;C&lt;/em&gt; is closely related to the existence of a discrete component of the corresponding Markov kernel &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, we also study mass distributions of Archimedean copulas. Building upon the interplay between Archimedean copulas and so-called Williamson measures we show how absolute continuity, discreteness and singularity of the Williamson measure propagates to the associated Archimedean copula. Moreover, considering the Lebesgue decomposition of the Markov kernel &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; as well as the measures induced by these components and the marginal &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, we prove that the subclass of Archimedean copulas for which all three measures have full support, is dense in &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;. Finally, viewing &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; in the light of Baire categories, we show that, in contrast to the space of bivari","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130523"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractional Sobolev embeddings and algebra property: A dyadic view","authors":"Patricia Alonso Ruiz ,&nbsp;Valentia Fragkiadaki","doi":"10.1016/j.jmaa.2026.130536","DOIUrl":"10.1016/j.jmaa.2026.130536","url":null,"abstract":"<div><div>This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> by means of Haar functions and dyadic decompositions. The aim is to provide an alternative, hands-on approach without Fourier transform that may be transferred to settings where the latter is not available. Explicit counterexamples are constructed to show the failure of the algebra property in the low-regularity regime.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130536"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gaussian estimates for general parabolic operators in dimension 1","authors":"Grégoire Nadin","doi":"10.1016/j.jmaa.2026.130484","DOIUrl":"10.1016/j.jmaa.2026.130484","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We derive in this paper Gaussian estimates for a general parabolic equation &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; over &lt;span&gt;&lt;math&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Here &lt;em&gt;a&lt;/em&gt; and &lt;em&gt;r&lt;/em&gt; are only assumed to be bounded, measurable and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;essinf&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. We first consider a canonical equation &lt;span&gt;&lt;math&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, with &lt;span&gt;&lt;math&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;em&gt;ν&lt;/em&gt; bounded and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;essinf&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, for which we derive Gaussian estimates for the fundamental solution:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mo&gt;∀&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; Here, the function &lt;em&gt;T&lt;/em&gt; is a corrector, for which we are able to derive appropriate properties using one-dimensional arguments. We then show that any solution &lt;em&gt;u&lt;/em&gt; of the original equation could be divided by some generalized principal eigenfunction &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; so that &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130484"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparison and distortion properties of new distance ratio metrics","authors":"Bibekananda Maji,&nbsp;Pritam Naskar,&nbsp;Swadesh Kumar Sahoo","doi":"10.1016/j.jmaa.2026.130480","DOIUrl":"10.1016/j.jmaa.2026.130480","url":null,"abstract":"<div><div>In 1979, Gehring and Osgood introduced the distance ratio metric, and later Vuorinen proposed another version of this metric. This manuscript investigates a new variant of these metrics defined on bounded domains in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>. We show that the metric <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span>, recently introduced by the authors, is the inner metric of one of the newly defined metrics corresponding to Vuorinen's version of the distance ratio metric. We also explore its relationships with several well-known hyperbolic-type metrics. The paper presents ball inclusion properties of the metrics associated with <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> and other hyperbolic-type metrics. Their distortion properties are also examined under several important classes of mappings. Furthermore, as an application, we demonstrate that these metrics can be used to characterize uniform domains.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130480"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiplicative partial isometries, manageability, and C⁎-algebraic quantum groupoids","authors":"Byung-Jay Kahng","doi":"10.1016/j.jmaa.2026.130535","DOIUrl":"10.1016/j.jmaa.2026.130535","url":null,"abstract":"<div><div>Generalizing the notion of a multiplicative unitary operator, which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a <em>multiplicative partial isometry</em>. The axioms include the pentagon equation, but more is needed. Under the “manageability” condition on a multiplicative partial isometry (modified from the Woronowicz's condition for a multiplicative unitary), it is possible to construct from it a pair of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras having almost the structure of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span><em>-algebraic quantum groupoid of separable type</em>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130535"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}