{"title":"μ-Hankel operators on compact Abelian groups","authors":"A. Mirotin","doi":"10.1007/s10476-023-0217-3","DOIUrl":null,"url":null,"abstract":"<div><p>(<i>μ</i>; <i>ν</i>)-Hankel operators between separable Hilbert spaces were introduced and studied recently (A. Mirotin and E. Kuzmenkova, <i>μ</i>-Hankel operators on Hilbert spaces, Opuscula Math., 41 (2021), 881–899). This paper is devoted to generalization of (<i>μ; ν</i>)-Hankel operators to the case of (non-separable in general) Hardy spaces over compact and connected Abelian groups. In this setting bounded (<i>μ</i>; <i>ν</i>)-Hankel operators are fully described under some natural conditions. Examples of integral operators are also considered.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 2","pages":"617 - 640"},"PeriodicalIF":0.6000,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0217-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0217-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
(μ; ν)-Hankel operators between separable Hilbert spaces were introduced and studied recently (A. Mirotin and E. Kuzmenkova, μ-Hankel operators on Hilbert spaces, Opuscula Math., 41 (2021), 881–899). This paper is devoted to generalization of (μ; ν)-Hankel operators to the case of (non-separable in general) Hardy spaces over compact and connected Abelian groups. In this setting bounded (μ; ν)-Hankel operators are fully described under some natural conditions. Examples of integral operators are also considered.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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