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Decoupling of modes for low regularity hyperbolic systems 低正则双曲系统的模式解耦
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-23 DOI: 10.1007/s13324-024-00982-3
Hart F. Smith
{"title":"Decoupling of modes for low regularity hyperbolic systems","authors":"Hart F. Smith","doi":"10.1007/s13324-024-00982-3","DOIUrl":"10.1007/s13324-024-00982-3","url":null,"abstract":"<div><p>We show that the coupling operator between distinct modes of a second-order hyperbolic system is smoothing of degree one, where we assume that the eigenvalues of the symbol are of constant rank, and that the coefficients of the system have bounded derivatives of second order. An important example is the wave equation for linear isotropic elasticity, where our assumption states that the Lamé parameters and mass density have bounded derivatives of second order. This extends a result for the elastic wave equation established by Brytik, et.al.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518987","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 the Hardy number of Koenigs domains 关于柯尼希斯域的哈代数
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-22 DOI: 10.1007/s13324-024-00981-4
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou, Luis Rodríguez-Piazza
{"title":"On the Hardy number of Koenigs domains","authors":"Manuel D. Contreras,&nbsp;Francisco J. Cruz-Zamorano,&nbsp;Maria Kourou,&nbsp;Luis Rodríguez-Piazza","doi":"10.1007/s13324-024-00981-4","DOIUrl":"10.1007/s13324-024-00981-4","url":null,"abstract":"<div><p>This work studies the Hardy number of hyperbolic planar domains satisfying Abel’s inclusion property, which are usually known as Koenigs domains. More explicitly, we prove that the Hardy number of a Koenings domains whose complement is non-polar is greater than or equal to 1/2, and this lower bound is sharp. In contrast to this result, we provide examples of general domains whose Hardy numbers are arbitrarily small. Additionally, we outline the connection of the aforementioned class of domains with the discrete dynamics of the unit disc and obtain results on the range of Hardy number of Koenigs maps, in the hyperbolic and parabolic case.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00981-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518427","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
Fractional Milne-type inequalities for twice differentiable functions for Riemann–Liouville fractional integrals 黎曼-刘维尔分式积分的二次微分函数的分式米尔恩型不等式
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-18 DOI: 10.1007/s13324-024-00980-5
Wali Haider, Hüseyin Budak, Asia Shehzadi
{"title":"Fractional Milne-type inequalities for twice differentiable functions for Riemann–Liouville fractional integrals","authors":"Wali Haider,&nbsp;Hüseyin Budak,&nbsp;Asia Shehzadi","doi":"10.1007/s13324-024-00980-5","DOIUrl":"10.1007/s13324-024-00980-5","url":null,"abstract":"<div><p>In this research, we investigate the error bounds associated with Milne’s formula, a well-known open Newton–Cotes approach, initially focused on differentiable convex functions within the frameworks of fractional calculus. Building on this work, we investigate fractional Milne-type inequalities, focusing on their application to the more refined class of twice-differentiable convex functions. This study effectively presents an identity involving twice differentiable functions and Riemann–Liouville fractional integrals. Using this newly established identity, we established error bounds for Milne’s formula in fractional and classical calculus. This study emphasizes the significance of convexity principles and incorporates the use of the Hölder inequality in formulating novel inequalities. In addition, we present precise mathematical illustrations to showcase the accuracy of the recently established bounds for Milne’s formula.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447437","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
Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times 关于伪对称和伪利玛窦对称广义罗伯逊-沃克时空的说明
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-14 DOI: 10.1007/s13324-024-00978-z
Abdallah Abdelhameed Syied, Uday Chand De, Nasser Bin Turki, Gabriel-Eduard Vîlcu
{"title":"Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times","authors":"Abdallah Abdelhameed Syied,&nbsp;Uday Chand De,&nbsp;Nasser Bin Turki,&nbsp;Gabriel-Eduard Vîlcu","doi":"10.1007/s13324-024-00978-z","DOIUrl":"10.1007/s13324-024-00978-z","url":null,"abstract":"<div><p>We establish two key results regarding pseudo symmetric and pseudo Ricci symmetric space-times. Firstly, we demonstrate that in pseudo symmetric generalized Robertson-Walker space-times either the scalar curvature remains constant or the associated vector field <span>(B_{i})</span> is irrotational. Secondly, in pseudo Ricci symmetric generalized Robertson-Walker space-times, we establish that either the scalar curvature is zero or the associated vector field <span>(A_{i})</span> is irrotational. We identify the conditions to ensure both <span>(B_{i})</span> and <span>(A_{i})</span> of these manifolds are acceleration-free and vorticity-free. We provide evidence that a pseudo symmetric and pseudo Ricci symmetric GRW space-time can be described as a perfect fluid. In a pseudo symmetric space-time, the state equation is given by <span>(p=frac{4-n}{ 2n-2}mu )</span>, whereas in a pseudo Ricci symmetric space-time, the state equation takes the form <span>(p=frac{3-n}{n-1}mu )</span>, where <i>p</i> and <span>(mu )</span> are the isotropic pressure and the energy density. It is noteworthy that if <span>(n=4)</span> , a pseudo symmetric space-time corresponds to the dust matter era, while a pseudo Ricci symmetric space-time corresponds to the phantom era.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00978-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431066","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
Weighted variable anisotropic Hardy spaces 加权变异各向异性哈代空间
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-14 DOI: 10.1007/s13324-024-00976-1
Yao He
{"title":"Weighted variable anisotropic Hardy spaces","authors":"Yao He","doi":"10.1007/s13324-024-00976-1","DOIUrl":"10.1007/s13324-024-00976-1","url":null,"abstract":"<div><p>In this paper, we introduce the weighted variable anisotropic Hardy spaces <span>(H_{omega ,A}^{p(cdot )}left( mathbb {R}^nright) )</span> via the nontangential grand maximal function. We also establish the atomic decompositions for the weighted variable anisotropic Hardy spaces <span>(H_{omega ,A}^{p(cdot )}left( mathbb {R}^nright) )</span>. In addition, we obtain the duality between <span>(H_{omega ,A}^{p(cdot )}left( mathbb {R}^nright) )</span> and the weighted anisotropic Campanato spaces with variable exponents. We also obtain equivalent characterizations of the weighted variable anisotropic Hardy spaces by means of the anisotropic Lusin area function, the Littlewood–Paley <i>g</i>-function and the Littlewood–Paley <span>(g_lambda ^*)</span>-function. As applications, we study the boundedness of Calderón–Zygmund singular integral operators on the weighted variable anisotropic Hardy spaces.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431041","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
Equidistribution for non-pluripolar currents with respect to holomorphic correspondences of compact Kähler manifolds 关于紧凑凯勒流形全形对应的非极性电流的等差数列
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-13 DOI: 10.1007/s13324-024-00977-0
Taeyong Ahn, Duc-Viet Vu
{"title":"Equidistribution for non-pluripolar currents with respect to holomorphic correspondences of compact Kähler manifolds","authors":"Taeyong Ahn,&nbsp;Duc-Viet Vu","doi":"10.1007/s13324-024-00977-0","DOIUrl":"10.1007/s13324-024-00977-0","url":null,"abstract":"<div><p>Let <i>X</i> be a compact Kähler manifold of complex dimension <span>(kge 2)</span> and <span>(f: X rightarrow X)</span> a holomorphic correspondence with simple action on cohomology such that <span>(f^{-1})</span> is also a holomorphic correspondence. We prove that the sequence of normalized pull-backs of a non-pluripolar current under iterates of <i>f</i> converges to the Green current associated with <i>f</i>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431054","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
Necessary and sufficient conditions for the quantitative weighted bounds of the Calderón type commutator for the Littlewood–Paley operator 利特尔伍德-帕利算子的卡尔德隆型换元的定量加权边界的必要条件和充分条件
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-10 DOI: 10.1007/s13324-024-00975-2
Yanping Chen, Xiaoxuan Chang, Teng Wang
{"title":"Necessary and sufficient conditions for the quantitative weighted bounds of the Calderón type commutator for the Littlewood–Paley operator","authors":"Yanping Chen,&nbsp;Xiaoxuan Chang,&nbsp;Teng Wang","doi":"10.1007/s13324-024-00975-2","DOIUrl":"10.1007/s13324-024-00975-2","url":null,"abstract":"<div><p>In this paper, we study the necessary and sufficient conditions for the quantitative weighted bounds of the Calderón type commutator for the Littlewood–Paley operator. Let <span>(g_{Omega ,1;b})</span> be the Calderón type commutator for the Littlewood–Paley operator where <span>(Omega )</span> is homogeneous of degree zero and satisfies the cancellation condition on the unit sphere, and <span>(bin Lip(mathbb {R}^n))</span>. More precisely, for the sufficiency, we use a new operator <span>(widetilde{G}_{Omega ,m;b}^j)</span>. Through the Calderón–Zygmund decomposition and the grand maximal operator <span>(mathcal {M}_{widetilde{G}_{Omega ,m;b}^j})</span> of weak type (1,1), we establish a sparse domination of <span>(widetilde{G}_{Omega ,m;b}^j)</span>. And then applying the interpolation theorem with change of measures and the relationship between the operators <span>(g_{Omega ,1;b})</span> and <span>(widetilde{G}_{Omega ,m;b}^j)</span>, we get the weighted bounds of the Calderón type commutators for the Littlewood–Paley operator <span>(g_{Omega ,1;b})</span>. In addition, for the necessity, through the local mean oscillation, we obtain Lip-type characterizations of <span>(Lip(mathbb {R}^n))</span> via the weighted bounds of the Calderón type commutators for the Littlewood–Paley operator.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411135","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
Differential subordination for bounded turning functions using pre-Schwarzian and the Schwarzian derivatives 使用前施瓦茨导数和施瓦茨导数的有界转折函数的微分从属关系
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-10 DOI: 10.1007/s13324-024-00973-4
Neenu Jose, V. Ravichandran, Abhijit Das
{"title":"Differential subordination for bounded turning functions using pre-Schwarzian and the Schwarzian derivatives","authors":"Neenu Jose,&nbsp;V. Ravichandran,&nbsp;Abhijit Das","doi":"10.1007/s13324-024-00973-4","DOIUrl":"10.1007/s13324-024-00973-4","url":null,"abstract":"<div><p>A normalized analytic function defined on the open unit disk is a bounded turning function if its derivative has positive real part. Such functions are univalent, and therefore, we find sufficient conditions for a function to be a bounded turning function. In this paper, we prove a general differential subordination theorem in terms of the derivative, the pre-Schwarzian derivative, and the Schwarzian derivative, providing sufficient conditions for a function to be a bounded turning function. We then apply the result to obtain several simple sufficient conditions.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411202","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 the Schatten exponent in orthonormal Strichartz estimate for the Dunkl operators 论邓克尔算子正交斯特里查兹估计中的沙腾指数
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-06 DOI: 10.1007/s13324-024-00970-7
Sunit Ghosh, Jitendriya Swain
{"title":"On the Schatten exponent in orthonormal Strichartz estimate for the Dunkl operators","authors":"Sunit Ghosh,&nbsp;Jitendriya Swain","doi":"10.1007/s13324-024-00970-7","DOIUrl":"10.1007/s13324-024-00970-7","url":null,"abstract":"<div><p>The orthonormal Strichartz estimates for the Schrödinger equation associated to the Dunkl Laplacian and the Dunkl-Hermite operator are derived in Senapati et al. (J Geom Anal 34:74, 2024) and Mondal and Song (Israel J Math, 2023). In this article we construct a set of coherent states in the Dunkl setting and apply semi-classical analysis to derive a necessary condition on the Schatten exponent for the aforementioned orthonormal Strichartz estimates, which turns out to be optimal for the Schrödinger equations associated with Laplacian and Hermite operator as a particular case.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410274","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
Dispersionless limit of the B-Toda hierarchy B-Toda 层次结构的无分散极限
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-06 DOI: 10.1007/s13324-024-00971-6
A. Zabrodin
{"title":"Dispersionless limit of the B-Toda hierarchy","authors":"A. Zabrodin","doi":"10.1007/s13324-024-00971-6","DOIUrl":"10.1007/s13324-024-00971-6","url":null,"abstract":"<div><p>We study the dispersionless limit of the recently introduced Toda lattice hierarchy with constraint of type B (the B-Toda hierarchy) and compare it with that of the DKP and C-Toda hierarchies. The dispersionless limits of the B-Toda and C-Toda hierarchies turn out to be the same.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410224","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
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