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On the second coefficient in the semi-classical expansion of toeplitz operators 关于toeplitz算子半经典展开中的第二系数
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-28 DOI: 10.1007/s13324-025-01105-2
Chin-Chia Chang, Hendrik Herrmann, Chin-Yu Hsiao
{"title":"On the second coefficient in the semi-classical expansion of toeplitz operators","authors":"Chin-Chia Chang,&nbsp;Hendrik Herrmann,&nbsp;Chin-Yu Hsiao","doi":"10.1007/s13324-025-01105-2","DOIUrl":"10.1007/s13324-025-01105-2","url":null,"abstract":"<div><p>Let <i>X</i> be a compact strictly pseudoconvex embeddable CR manifold and let <i>A</i> be the Toeplitz operator on <i>X</i> associated with a Reeb vector field <span>({mathcal {T}}in {mathscr {C}}^infty (X,TX))</span>. Consider the operator <span>(chi _k(A))</span> defined by the functional calculus of <i>A</i>, where <span>(chi )</span> is a smooth function with compact support in the positive real line and <span>(chi _k(lambda ):=chi (k^{-1}lambda ))</span>. It was established recently that <span>(chi _k(A)(x,y))</span> admits a full asymptotic expansion in <i>k</i> when <span>(k)</span> becomes large. The second coefficient of the expansion plays an important role in the further studies of CR geometry. In this work, we calculate the second coefficient of the expansion.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01105-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171117","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
Squared basis operators related to Bessel functions 与贝塞尔函数相关的平方基算子
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-26 DOI: 10.1007/s13324-025-01110-5
Monika Herzog
{"title":"Squared basis operators related to Bessel functions","authors":"Monika Herzog","doi":"10.1007/s13324-025-01110-5","DOIUrl":"10.1007/s13324-025-01110-5","url":null,"abstract":"<div><p>Recent studies on linear positive operators have led to the investigation of approximation properties of Szász–Mirkyan operators related to the modified Bessel function of order 0. In this paper, we analyse the asymptotic behavior of these operators, convergence theorems, Voronovskaya and Grüss-Voronovskaya type results. A comparative assessment with classical Szász–Mirakyan operators is also presented. These results may have an impact on wide branches of knowledge, such as probability theory, statistics, physical chemistry, optics, and computer science, especially signal processing.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01110-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170402","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
Two-dimensional Calderón problem and flat metrics 二维Calderón问题和平面度量
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-24 DOI: 10.1007/s13324-025-01112-3
Vladimir A. Sharafutdinov
{"title":"Two-dimensional Calderón problem and flat metrics","authors":"Vladimir A. Sharafutdinov","doi":"10.1007/s13324-025-01112-3","DOIUrl":"10.1007/s13324-025-01112-3","url":null,"abstract":"<div><p>For a compact Riemannian manifold (<i>M</i>, <i>g</i>) with boundary <span>(partial M)</span>, the Dirichlet-to-Neumann operator <span>(Lambda _g:C^infty (partial M)longrightarrow C^infty (partial M))</span> is defined by <span>(Lambda _gf=left. frac{partial u}{partial nu }right| _{partial M})</span>, where <span>(nu )</span> is the unit outer normal vector to the boundary and <i>u</i> is the solution to the Dirichlet problem <span>(Delta _gu=0, u|_{partial M}=f)</span>. Let <span>(g_partial )</span> be the Riemannian metric on <span>(partial M)</span> induced by <i>g</i>. The Calderón problem is posed as follows: To what extent is (<i>M</i>, <i>g</i>) determined by the data <span>((partial M,g_partial ,Lambda _g))</span>? We prove the uniqueness theorem: A compact connected two-dimensional Riemannian manifold (<i>M</i>, <i>g</i>) with non-empty boundary is determined by the data <span>((partial M,g_partial ,Lambda _g))</span> uniquely up to conformal equivalence.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168076","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
A study on the nonexistence of stable solutions for nonlinear elliptic equations in strips 条形非线性椭圆方程稳定解的不存在性研究
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-17 DOI: 10.1007/s13324-025-01107-0
Cherif Zaidi
{"title":"A study on the nonexistence of stable solutions for nonlinear elliptic equations in strips","authors":"Cherif Zaidi","doi":"10.1007/s13324-025-01107-0","DOIUrl":"10.1007/s13324-025-01107-0","url":null,"abstract":"<div><p>In this paper, we investigate the nonexistence of solutions of certain nonlinear elliptic equations, focusing on solutions that are stable or stable outside a compact set, potentially unbounded, and sign-changing. Our primary methods include integral estimates, Pohozaev-type identity and the monotonicity formula. Our classification approaches as a sharp result, specifically, in the subcritical case (i.e, <span>(1&lt; p &lt; frac{n+4}{n-4})</span>), we establish the existence of a mountain pass solution with a Morse index of 1 in the subspace of <span>(H^2 cap H_0^1(Omega ))</span> that exhibits cylindrical symmetry.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165835","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 versions of Hermite–Hadamard inequalities on Discrete Time Scales 离散时间尺度上Hermite-Hadamard不等式的新版本
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-16 DOI: 10.1007/s13324-025-01106-1
Hüseyin Budak
{"title":"New versions of Hermite–Hadamard inequalities on Discrete Time Scales","authors":"Hüseyin Budak","doi":"10.1007/s13324-025-01106-1","DOIUrl":"10.1007/s13324-025-01106-1","url":null,"abstract":"<div><p>In this paper, we first introduced two time scales based on the interval [<i>a</i>, <i>b</i>] and <span>( mathbb {Z} )</span>. Then, by using one of these time scale and substitutions rules, we prove a new version of discrete Hermite-Hadamard inequality for discrete convex functions. Moreover, we investigate the fractional version of this inequality involving fractional delta and nabla sums.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166243","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
Existence theorems for PDEs modeling erosion and the optimal transportation of sediment PDEs模拟侵蚀和泥沙最优输运的存在定理
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-15 DOI: 10.1007/s13324-025-01100-7
Björn Birnir, Therese Basa Landry
{"title":"Existence theorems for PDEs modeling erosion and the optimal transportation of sediment","authors":"Björn Birnir,&nbsp;Therese Basa Landry","doi":"10.1007/s13324-025-01100-7","DOIUrl":"10.1007/s13324-025-01100-7","url":null,"abstract":"<div><p>We prove the existence of unique global weak solutions to equations describing the sediment flow in the evolution of fluvial land surfaces, with constant water depth. These equations describe the so-called transport-limited situation, where all the sediment can be transported away given enough water. This is in distinction to the detachment-limited situation where we must wait for rock to weather (to sediment) before it can be transported away. Earlier work shows that these equations describe the optimal transport of sediment and the evolution of the surfaces in optimal transport theory. The existence theory is also extended to include diffusion in the water and the land surfaces.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01100-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166237","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
The dimension of planar elliptic measures arising from Lipschitz matrices in Reifenberg flat domains 赖芬贝格平面域中由Lipschitz矩阵产生的平面椭圆测度的维数
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-12 DOI: 10.1007/s13324-025-01067-5
Ignasi Guillén-Mola, Martí Prats, Xavier Tolsa
{"title":"The dimension of planar elliptic measures arising from Lipschitz matrices in Reifenberg flat domains","authors":"Ignasi Guillén-Mola,&nbsp;Martí Prats,&nbsp;Xavier Tolsa","doi":"10.1007/s13324-025-01067-5","DOIUrl":"10.1007/s13324-025-01067-5","url":null,"abstract":"<div><p>In this paper we show that, given a planar Reifenberg flat domain with small constant and a divergence form operator associated to a real (not necessarily symmetric) uniformly elliptic matrix with Lipschitz coefficients, the Hausdorff dimension of its elliptic measure is at most 1. More precisely, we prove that there exists a subset of the boundary with full elliptic measure and with <span>(sigma )</span>-finite one-dimensional Hausdorff measure. For Reifenberg flat domains, this result extends a previous work of Thomas H. Wolff for the harmonic measure.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01067-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165197","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
Generalized fractional integral operators on Morrey spaces and their bi-preduals Morrey空间上的广义分数积分算子及其双preduals
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-11 DOI: 10.1007/s13324-025-01091-5
Satoshi Yamaguchi, Eiichi Nakai
{"title":"Generalized fractional integral operators on Morrey spaces and their bi-preduals","authors":"Satoshi Yamaguchi,&nbsp;Eiichi Nakai","doi":"10.1007/s13324-025-01091-5","DOIUrl":"10.1007/s13324-025-01091-5","url":null,"abstract":"<div><p>In this paper we prove the boundedness of the generalized fractional integral operator <span>(I_{rho })</span> on generalized Morrey spaces with variable growth condition, which is an improvement of previous results, and then, we establish the boundedness of <span>(I_{rho })</span> on their bi-preduals. We also prove the boundedness of <span>(I_{rho })</span> on their preduals by the duality.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163792","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
Besov–Bourgain–Morrey–Campanato Spaces: Boundedness of Operators, Duality, and Sharp John–Nirenberg Inequality Besov-Bourgain-Morrey-Campanato空间：算子的有界性、对偶性和Sharp John-Nirenberg不等式
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-11 DOI: 10.1007/s13324-025-01078-2
Ying Jin, Yinqin Li, Dachun Yang
{"title":"Besov–Bourgain–Morrey–Campanato Spaces: Boundedness of Operators, Duality, and Sharp John–Nirenberg Inequality","authors":"Ying Jin,&nbsp;Yinqin Li,&nbsp;Dachun Yang","doi":"10.1007/s13324-025-01078-2","DOIUrl":"10.1007/s13324-025-01078-2","url":null,"abstract":"<div><p>Bourgain–Morrey spaces, introduced by J. Bourgain, play an important role in the analysis of some linear and nonlinear partial differential equations. In this article, by exploiting the exquisite geometrical structure of shifted dyadic systems in the Euclidean space, we introduce (dyadic) Besov–Bourgain–Morrey–Campanato spaces via innovatively mixing together both the integral means from Campanato spaces and the structural framework of Besov–Bourgain–Morrey spaces (a recent generalization of Bourgain–Morrey spaces). We then study their fundamental real-variable properties, including the triviality and the nontriviality, their relations with other known function spaces, their predual spaces, as well as sharp John–Nirenberg type inequalities with distinct necessary and sufficient conditions which are different from the case of BMO and Campanato spaces. In particular, after establishing an equivalent quasi-norm of non-dyadic Besov–Bourgain–Morrey–Campanato spaces expressed via integrals, we characterize the boundedness of both Calderón–Zygmund operators and generalized fractional integrals on these non-dyadic function spaces and their predual spaces via vanishing conditions.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165161","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 a unique two-dimensional integral operator homogeneous with respect to all orientation preserving linear transformations 在一个唯一的二维积分算子上对所有保持方向的线性变换齐次
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-07-10 DOI: 10.1007/s13324-025-01104-3
Zhirayr Avetisyan, Alexey Karapetyants, Adolf Mirotin
{"title":"On a unique two-dimensional integral operator homogeneous with respect to all orientation preserving linear transformations","authors":"Zhirayr Avetisyan,&nbsp;Alexey Karapetyants,&nbsp;Adolf Mirotin","doi":"10.1007/s13324-025-01104-3","DOIUrl":"10.1007/s13324-025-01104-3","url":null,"abstract":"<div><p>In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of general homogeneous operators. This is the unique two-dimensional operator that has an antisymmetric kernel homogeneous with respect to all orientation-preserving linear transformations of the plane. It is shown that the operator under consideration interacts naturally, both in Cartesian and polar coordinates, with projective tensor products of some classical functional spaces, such as Lebesgue, Hardy, and Hölder spaces; conditions for their boundedness as operators acting from these spaces to Banach lattices of measurable functions and estimates of their norms are given.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164283","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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