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Localization operators on discrete Orlicz modulation spaces 离散奥利兹调制空间上的定位算子
arXiv - MATH - Functional Analysis Pub Date : 2024-09-09 DOI: arxiv-2409.05373
Aparajita Dasgupta, Anirudha Poria
{"title":"Localization operators on discrete Orlicz modulation spaces","authors":"Aparajita Dasgupta, Anirudha Poria","doi":"arxiv-2409.05373","DOIUrl":"https://doi.org/arxiv-2409.05373","url":null,"abstract":"In this paper, we introduce Orlicz spaces on $ mathbb Z^n times mathbb T^n\u0000$ and Orlicz modulation spaces on $mathbb Z^n$, and present some basic\u0000properties such as inclusion relations, convolution relations, and duality of\u0000these spaces. We show that the Orlicz modulation space $M^{Phi}(mathbb Z^n)$\u0000is close to the modulation space $M^{2}(mathbb Z^n)$ for some particular Young\u0000function $Phi$. Then, we study a class of pseudo-differential operators known\u0000as time-frequency localization operators on $mathbb Z^n$, which depend on a\u0000symbol $varsigma$ and two windows functions $g_1$ and $g_2$. Using appropriate\u0000classes for symbols, we study the boundedness of the localization operators on\u0000Orlicz modulation spaces on $mathbb Z^n$. Also, we show that these operators\u0000are compact and in the Schatten--von Neumann classes.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
No-dimensional Helly's theorem in uniformly convex Banach spaces 均匀凸巴拿赫空间中的无维赫里定理
arXiv - MATH - Functional Analysis Pub Date : 2024-09-09 DOI: arxiv-2409.05744
G. Ivanov
{"title":"No-dimensional Helly's theorem in uniformly convex Banach spaces","authors":"G. Ivanov","doi":"arxiv-2409.05744","DOIUrl":"https://doi.org/arxiv-2409.05744","url":null,"abstract":"We study the ``no-dimensional'' analogue of Helly's theorem in Banach spaces.\u0000Specifically, we obtain the following no-dimensional Helly-type results for\u0000uniformly convex Banach spaces: Helly's theorem, fractional Helly's theorem,\u0000colorful Helly's theorem, and colorful fractional Helly's theorem. The combinatorial part of the proofs for these Helly-type results is\u0000identical to the Euclidean case as presented in cite{adiprasito2020theorems}.\u0000The primary difference lies in the use of a certain geometric inequality in\u0000place of the Pythagorean theorem. This inequality can be explicitly expressed\u0000in terms of the modulus of convexity of a Banach space.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The heat semigroup associated with the Jacobi--Cherednik operator and its applications 与雅可比-切列德尼克算子相关的热半群及其应用
arXiv - MATH - Functional Analysis Pub Date : 2024-09-09 DOI: arxiv-2409.05376
Anirudha Poria, Ramakrishnan Radha
{"title":"The heat semigroup associated with the Jacobi--Cherednik operator and its applications","authors":"Anirudha Poria, Ramakrishnan Radha","doi":"arxiv-2409.05376","DOIUrl":"https://doi.org/arxiv-2409.05376","url":null,"abstract":"In this paper, we study the heat equation associated with the\u0000Jacobi--Cherednik operator on the real line. We establish some basic properties\u0000of the Jacobi--Cherednik heat kernel and heat semigroup. We also provide a\u0000solution to the Cauchy problem for the Jacobi--Cherednik heat operator and\u0000prove that the heat kernel is strictly positive. Then, we characterize the\u0000image of the space $L^2(mathbb R, A_{alpha, beta})$ under the\u0000Jacobi--Cherednik heat semigroup as a reproducing kernel Hilbert space. As an\u0000application, we solve the modified Poisson equation and present the\u0000Jacobi--Cherednik--Markov processes.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conditional bases with Property~(A) 带属性的条件基~(A)
arXiv - MATH - Functional Analysis Pub Date : 2024-09-07 DOI: arxiv-2409.04883
Fernando Albiac, Jose L. Ansorena, Pablo Berná, Miguel Berasategui
{"title":"Conditional bases with Property~(A)","authors":"Fernando Albiac, Jose L. Ansorena, Pablo Berná, Miguel Berasategui","doi":"arxiv-2409.04883","DOIUrl":"https://doi.org/arxiv-2409.04883","url":null,"abstract":"Property~(A) is a week symmetry condition that plays a fundamental role in\u0000the characterization of greedy-type bases in the isometric case, i.e., when the\u0000constants involved in the study of the efficiency of the thresholding greedy\u0000algorithm in Banach spaces are sharp. In this note we build examples of Banach\u0000spaces with Schauder bases that have Property~(A) but fail to be unconditional,\u0000thus settling a long standing problem in the area. As a by-product of our work\u0000we hone our construction to produce counterexamples that solve other open\u0000questions in the isometric theory of greedy bases.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"252 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Isomorphisms between vector-valued $H_p$-spaces for $0 $0 的矢量值 $H_p$ 空间之间的同构关系
arXiv - MATH - Functional Analysis Pub Date : 2024-09-07 DOI: arxiv-2409.04866
Fernando Albiac, Jose L. Ansorena
{"title":"Isomorphisms between vector-valued $H_p$-spaces for $0","authors":"Fernando Albiac, Jose L. Ansorena","doi":"arxiv-2409.04866","DOIUrl":"https://doi.org/arxiv-2409.04866","url":null,"abstract":"The aim of this paper is twofold. On the one hand, we manage to identify\u0000Banach-valued Hardy spaces of analytic functions over the disc $mathbb{D}$\u0000with other classes of Hardy spaces, thus complementing the existing literature\u0000on the subject. On the other hand, we develop new techniques that allow us to\u0000prove that certain Hilbert-valued atomic lattices have a unique unconditional\u0000basis, up to normalization, equivalence and permutation. Combining both lines\u0000of action we show that that $H_p(mathbb{D},ell_2)$ for $0<p<1$ has a unique\u0000atomic lattice structure. The proof of this result relies on the validity of\u0000some new lattice estimates for non-locally convex spaces which hold an\u0000independent interest.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Besov spaces and Schatten class Hankel operators on Paley--Wiener spaces of convex domains 凸域的 Paley-Wiener 空间上的 Besov 空间和 Schatten 类汉克尔算子
arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI: arxiv-2409.04184
Konstantinos Bampouras, Karl-Mikael Perfekt
{"title":"Besov spaces and Schatten class Hankel operators on Paley--Wiener spaces of convex domains","authors":"Konstantinos Bampouras, Karl-Mikael Perfekt","doi":"arxiv-2409.04184","DOIUrl":"https://doi.org/arxiv-2409.04184","url":null,"abstract":"We consider Schatten class membership of multi-parameter Hankel operators on\u0000the Paley--Wiener space of a bounded convex domain $Omega$. For admissible\u0000domains, we develop a framework and theory of Besov spaces of Paley--Wiener\u0000type. We prove that a Hankel operator belongs to the Schatten class $S^p$ if\u0000and only if its symbol belongs to a corresponding Besov space, for $1 leq p\u0000leq 2$. For smooth domains $Omega$ with positive curvature, we extend this\u0000result to $1 leq p < 4$, and for simple polytopes to the full range $1 leq p\u0000< infty$.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Random Geometric Graphs in Reflexive Banach Spaces 反身巴拿赫空间中的随机几何图形
arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI: arxiv-2409.04237
József Balogh, Mark Walters, András Zsák
{"title":"Random Geometric Graphs in Reflexive Banach Spaces","authors":"József Balogh, Mark Walters, András Zsák","doi":"arxiv-2409.04237","DOIUrl":"https://doi.org/arxiv-2409.04237","url":null,"abstract":"We investigate a random geometric graph model introduced by Bonato and\u0000Janssen. The vertices are the points of a countable dense set $S$ in a\u0000(necessarily separable) normed vector space $X$, and each pair of points are\u0000joined independently with some fixed probability $p$ (with $0<p<1$) if they are\u0000less than distance $1$ apart. A countable dense set $S$ in a normed space is\u0000Rado, if the resulting graph is almost surely unique up to isomorphism: that is\u0000any two such graphs are, almost surely, isomorphic. Not surprisingly, understanding which sets are Rado is closely related to the\u0000geometry of the underlying normed space. It turns out that a key question is in\u0000which spaces must step-isometries (maps that preserve the integer parts of\u0000distances) on dense subsets necessarily be isometries. We answer this question\u0000for a large class of Banach spaces including all strictly convex reflexive\u0000spaces. In the process we prove results on the interplay between the norm\u0000topology and weak topology that may be of independent interest. As a consequence of these Banach space results we show that almost all\u0000countable dense sets in strictly convex reflexive spaces are strongly non-Rado\u0000(that is, any two graphs are almost surely non-isomorphic). However, we show\u0000that there do exist Rado sets even in $ell_2$. Finally we construct a Banach\u0000spaces in which all countable dense set are strongly non-Rado.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rate of growth of random analytic functions, with an application to linear dynamics 随机解析函数的增长率，在线性动力学中的应用
arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI: arxiv-2409.04235
Kevin Agneessens, Karl-G. Grosse-Erdmann
{"title":"Rate of growth of random analytic functions, with an application to linear dynamics","authors":"Kevin Agneessens, Karl-G. Grosse-Erdmann","doi":"arxiv-2409.04235","DOIUrl":"https://doi.org/arxiv-2409.04235","url":null,"abstract":"We obtain Wiman-Valiron type inequalities for random entire functions and for\u0000random analytic functions on the unit disk that improve a classical result of\u0000ErdH{o}s and R'enyi and recent results of Kuryliak and Skaskiv. Our results\u0000are then applied to linear dynamics: we obtain rates of growth, outside some\u0000exceptional set, for analytic functions that are frequently hypercyclic for an\u0000arbitrary chaotic weighted backward shift.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"453 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On extremal nonexpansive mappings 关于极值非展开映射
arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI: arxiv-2409.04292
Christian Bargetz, Michael Dymond, Katriin Pirk
{"title":"On extremal nonexpansive mappings","authors":"Christian Bargetz, Michael Dymond, Katriin Pirk","doi":"arxiv-2409.04292","DOIUrl":"https://doi.org/arxiv-2409.04292","url":null,"abstract":"We study the extremality of nonexpansive mappings on a nonempty bounded\u0000closed and convex subset of a normed space (therein specific Banach spaces). We\u0000show that surjective isometries are extremal in this sense for many Banach\u0000spaces, including Banach spaces with the Radon-Nikodym property and all\u0000$C(K)$-spaces for compact Hausdorff $K.$ We also conclude that the typical, in\u0000the sense of Baire category, nonexpansive mapping is close to being extremal.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"73 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Periodic solutions to nonlocal pseudo-differential equations. A bifurcation theoretical perspective 非局部伪微分方程的周期解。分岔理论视角
arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI: arxiv-2409.04253
Juan Carlos Sampedro
{"title":"Periodic solutions to nonlocal pseudo-differential equations. A bifurcation theoretical perspective","authors":"Juan Carlos Sampedro","doi":"arxiv-2409.04253","DOIUrl":"https://doi.org/arxiv-2409.04253","url":null,"abstract":"In this paper we use abstract bifurcation theory for Fredholm operators of\u0000index zero to deal with periodic even solutions of the one-dimensional equation\u0000$mathcal{L}u=lambda u+|u|^{p}$, where $mathcal{L}$ is a nonlocal\u0000pseudodifferential operator defined as a Fourier multiplier and $lambda$ is\u0000the bifurcation parameter. Our general setting includes the fractional\u0000Laplacian $mathcal{L}equiv(-Delta)^{s}$ and sharpens the results obtained\u0000for this operator to date. As a direct application, we establish the existence\u0000of traveling waves for general nonlocal dispersive equations for some velocity\u0000ranges.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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