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Inverse scattering problems for the Dirac operator on the line with partial knowledge of the potential
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-13 DOI: 10.1007/s13324-025-01029-x
Ying Yang, Haiyan Jin, Guangsheng Wei
{"title":"Inverse scattering problems for the Dirac operator on the line with partial knowledge of the potential","authors":"Ying Yang,&nbsp;Haiyan Jin,&nbsp;Guangsheng Wei","doi":"10.1007/s13324-025-01029-x","DOIUrl":"10.1007/s13324-025-01029-x","url":null,"abstract":"<div><p>The inverse scattering problem for the Dirac equation on the real line are considered. It is shown that the potential on the real line is uniquely determined in terms of the mixed scattering data which consists of the knowledge of the potential on the right (left) half line of the real axis and the reflection coefficient from the right (left). In particular, neither the bound states or the bound state norming constants are needed. The method is based on a factorization of a scattering matrix.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396479","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}
引用次数: 0
Normality concerning the sequence of multiple functions
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-10 DOI: 10.1007/s13324-025-01024-2
Dongmei Wei, Fei Li, Yan Xu
{"title":"Normality concerning the sequence of multiple functions","authors":"Dongmei Wei,&nbsp;Fei Li,&nbsp;Yan Xu","doi":"10.1007/s13324-025-01024-2","DOIUrl":"10.1007/s13324-025-01024-2","url":null,"abstract":"<div><p>Let <span>({f_n})</span> be a sequence of meromorphic functions defined in a domain <i>D</i>, and let <span>({psi _n})</span> be a sequence of holomorphic functions on <i>D</i>, whose zeros are multiple, such that <span>(psi _nrightarrow psi )</span> converges locally uniformly in <i>D</i>, where <span>(psi (not equiv 0))</span> is holomorphic in <i>D</i>. If, (1) <span>(f_nne 0)</span> and <span>(f_n^{(k)}ne 0)</span>; (2) all zeros of <span>(f_n^{(k)}-psi _n)</span> have multiplicities at least <span>((k+2)/k)</span>, then <span>({f_n})</span> is normal in <i>D</i>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373342","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}
引用次数: 0
Pointwise approximation on the Alice Roth’s Swiss cheese
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1007/s13324-025-01026-0
Eduardo S. Zeron, Jesús Emmanuel Castillo
{"title":"Pointwise approximation on the Alice Roth’s Swiss cheese","authors":"Eduardo S. Zeron,&nbsp;Jesús Emmanuel Castillo","doi":"10.1007/s13324-025-01026-0","DOIUrl":"10.1007/s13324-025-01026-0","url":null,"abstract":"<div><p>We show that the complex conjugate function <span>(zmapsto overline{z})</span> cannot be <i>pointwise</i> approximated by holomorphic polynomials on the Alice Roth’s Swiss cheese <span>(Q_Rsubset mathbb {C})</span>. Moreover, under some extra hypotheses, we also show that the complex conjugate cannot be <i>pointwise</i> approximated either by functions holomorphic on <span>(Q_R)</span>.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01026-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of normalized solutions to a class of non-autonomous (p, q)-Laplacian equations
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-08 DOI: 10.1007/s13324-025-01025-1
Xiaoxiao Cui, Anran Li, Chongqing Wei
{"title":"Existence of normalized solutions to a class of non-autonomous (p, q)-Laplacian equations","authors":"Xiaoxiao Cui,&nbsp;Anran Li,&nbsp;Chongqing Wei","doi":"10.1007/s13324-025-01025-1","DOIUrl":"10.1007/s13324-025-01025-1","url":null,"abstract":"<div><p>We study the multiplicity of normalized solutions of the following (<i>p</i>, <i>q</i>)-Laplacian equation </p><div><div><span>$$begin{aligned} left{ begin{array}{ll} -Delta _p u-Delta _q u=lambda |u|^{p-2}u+V(epsilon x)f(u) text {in} mathbb {R}^N, int _{mathbb {R}^N}|u|^pdx=a^p, end{array}right. end{aligned}$$</span></div></div><p>where <span>(1&lt;p&lt;q&lt;N)</span>, <i>a</i>, <span>(epsilon &gt;0)</span>, <span>(Delta _lu:=hbox {div}(|nabla u|^{l-2}nabla u))</span> with <span>(lin {p,q})</span>, stands for the <i>l</i>-Laplacian operator. <span>(lambda in mathbb {R})</span> is an unknown parameter that appears as a Lagrange multiplier. <span>(V:mathbb {R}^Nrightarrow mathbb {R})</span> is a continuous function with some proper assumptions. <i>f</i> is a continuous function with <span>(L^p)</span>-mass subcritical growth. By using variational methods, we prove that the equation has multiple normalized solutions, as <span>(epsilon )</span> is small enough. Precisely, the number of normalized solutions is at least twice that of the global maximum points of <i>V</i>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361847","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}
引用次数: 0
Banach Lie groupoid of partial isometries over the restricted Grassmannian
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-08 DOI: 10.1007/s13324-025-01028-y
Tomasz Goliński, Grzegorz Jakimowicz, Aneta Sliżewska
{"title":"Banach Lie groupoid of partial isometries over the restricted Grassmannian","authors":"Tomasz Goliński,&nbsp;Grzegorz Jakimowicz,&nbsp;Aneta Sliżewska","doi":"10.1007/s13324-025-01028-y","DOIUrl":"10.1007/s13324-025-01028-y","url":null,"abstract":"<div><p>The set of partial isometries in a <span>(W^*)</span>-algebra possesses a structure of Banach Lie groupoid. In this paper, the differential structure on the set of partial isometries over the restricted Grassmannian is constructed, which makes it into a Banach Lie groupoid.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361936","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}
引用次数: 0
Lipschitz shadowing for contracting/expanding dynamics on average
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-08 DOI: 10.1007/s13324-025-01022-4
Lucas Backes, Davor Dragičević
{"title":"Lipschitz shadowing for contracting/expanding dynamics on average","authors":"Lucas Backes,&nbsp;Davor Dragičević","doi":"10.1007/s13324-025-01022-4","DOIUrl":"10.1007/s13324-025-01022-4","url":null,"abstract":"<div><p>We prove that Lipschitz perturbations of nonautonomous contracting or expanding linear dynamics are Lipschitz shadowable provided that the Lipschitz constants are small on average. This is in sharp contrast with previous results where the Lipschitz constants are assumed to be uniformly small. Moreover, we show by means of an example that a natural extension of these results to the context of linear dynamics admitting an exponential dichotomy does not hold in general.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361841","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}
引用次数: 0
Non-invariant infinitely connected cycle of Baker domains
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-08 DOI: 10.1007/s13324-025-01021-5
Janina Kotus, Marco Montes de Oca Balderas
{"title":"Non-invariant infinitely connected cycle of Baker domains","authors":"Janina Kotus,&nbsp;Marco Montes de Oca Balderas","doi":"10.1007/s13324-025-01021-5","DOIUrl":"10.1007/s13324-025-01021-5","url":null,"abstract":"<div><p>We give the first example of a non-invariant cycle of Baker domains of infinite connectivity for non-entire meromorphic functions. We also prove the necessary and sufficient condition for a cycle of Baker domains to be infinitely connected in terms of critical points for the family <span>(f(z)=lambda e^z+frac{mu }{z})</span>, where <span>(lambda )</span> and <span>(mu )</span> are defined in the paper.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361935","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}
引用次数: 0
New fractional type weights and the boundedness of some operators
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-07 DOI: 10.1007/s13324-025-01027-z
Xi Cen, Qianjun He, Zichen Song, Zihan Wang
{"title":"New fractional type weights and the boundedness of some operators","authors":"Xi Cen,&nbsp;Qianjun He,&nbsp;Zichen Song,&nbsp;Zihan Wang","doi":"10.1007/s13324-025-01027-z","DOIUrl":"10.1007/s13324-025-01027-z","url":null,"abstract":"<div><p>Two classes of fractional type variable weights are established in this paper. The first kind of weights <span>({A_{vec { p}( cdot ),q( cdot )}})</span> are variable multiple weights, which are characterized by the weighted variable boundedness of multilinear fractional type operators, called multilinear Hardy–Littlewood–Sobolev theorem on weighted variable Lebesgue spaces. Meanwhile, the weighted variable boundedness for the commutators of multilinear fractional type operators are also obtained. This generalizes some known work, such as Moen (Collect Math 60(2):213–238, 2009), Bernardis et al. (Ann Acad Sci Fenn-M 39:23–50, 2014), and Cruz-Uribe and Guzmán (Publ Mat 64(2):453–498, 2020). Another class of weights <span>({{mathbb {A}}_{p( cdot ),q(cdot )}})</span> are variable matrix weights that also characterized by certain fractional type operators. This generalize some previous results on matrix weights <span>({{mathbb {A}}_{p( cdot )}})</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361877","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}
引用次数: 0
On classical orthogonal polynomials on bi-lattices
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-05 DOI: 10.1007/s13324-025-01023-3
K. Castillo, G. Filipuk, D. Mbouna
{"title":"On classical orthogonal polynomials on bi-lattices","authors":"K. Castillo,&nbsp;G. Filipuk,&nbsp;D. Mbouna","doi":"10.1007/s13324-025-01023-3","DOIUrl":"10.1007/s13324-025-01023-3","url":null,"abstract":"<div><p>In Vinet and Zhedanov (J Phys A Math Theor 45:265304, 2012), while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomials, that they called para-Krawtchouk polynomials, defined on a bilinear lattice. In this note we present necessary and sufficient conditions for the regularity of solutions of the corresponding functional equation. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented. As a consequence, we characterize all solutions of the functional equation, including as very particular cases the Meixner, Charlier, Krawtchouk, Hahn, and para-Krawtchouk polynomials.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108385","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}
引用次数: 0
Generalized Riesz potential operators on Musielak–Orlicz–Morrey spaces over unbounded metric measure spaces
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-04 DOI: 10.1007/s13324-025-01020-6
Takao Ohno, Tetsu Shimomura
{"title":"Generalized Riesz potential operators on Musielak–Orlicz–Morrey spaces over unbounded metric measure spaces","authors":"Takao Ohno,&nbsp;Tetsu Shimomura","doi":"10.1007/s13324-025-01020-6","DOIUrl":"10.1007/s13324-025-01020-6","url":null,"abstract":"<div><p>In this paper we discuss the boundedness of the Hardy–Littlewood maximal operator <span>(M_{lambda }, lambda ge 1)</span>, and the variable Riesz potential operator <span>(I_{alpha (cdot ),tau }, tau ge 1)</span>, on Musielak–Orlicz–Morrey spaces <span>(L^{Phi ,kappa ,theta }(X))</span> over unbounded metric measure spaces <i>X</i>. As an important example, we obtain the boundedness of <span>(M_{lambda })</span> and <span>(I_{alpha (cdot ),tau })</span> in the framework of double phase functionals with variable exponents <span>(Phi (x,t) = t^{p(x)} + a(x) t^{q(x)}, x in X, t ge 0)</span>, where <span>(p(x)&lt;q(x))</span> for <span>(xin X)</span>, <span>(a(cdot ))</span> is a non-negative, bounded and Hölder continuous function of order <span>(theta in (0,1])</span>. Our results are new even for the variable exponent Morrey spaces or for the doubling metric measure case in that the underlying spaces need not be bounded.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01020-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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