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001451471 001__ 1451471
001451471 003__ OCoLC
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001451471 019__ $$a1351749286$$a1354569981$$a1355231451
001451471 020__ $$a9783031144592$$q(electronic bk.)
001451471 020__ $$a3031144597$$q(electronic bk.)
001451471 020__ $$z9783031144585
001451471 020__ $$z3031144589
001451471 0247_ $$a10.1007/978-3-031-14459-2$$2doi
001451471 035__ $$aSP(OCoLC)1351732125
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001451471 1001_ $$aPersson, Lars-Erik,$$d1944-$$eauthor.$$1https://isni.org/isni/0000000109709313
001451471 24510 $$aMartingale Hardy spaces and summability of one-dimensional Vilenkin-Fourier series /$$cLars-Erik Persson, George Tephnadze, Ferenc Weisz.
001451471 264_1 $$aCham :$$bBirkhäuser,$$c[2022]
001451471 264_4 $$c©2022
001451471 300__ $$a1 online resource (xvi, 626 pages)
001451471 336__ $$atext$$btxt$$2rdacontent
001451471 337__ $$acomputer$$bc$$2rdamedia
001451471 338__ $$aonline resource$$bcr$$2rdacarrier
001451471 504__ $$aIncludes bibliographical references and index.
001451471 5050_ $$aIntro -- Preface -- How to Read the Book? -- Acknowledgements -- Contents -- 1 Partial Sums of Vilenkin-Fourier Series in Lebesgue Spaces -- 1.1 Introduction -- 1.2 Vilenkin Groups and Functions -- 1.3 The Representation of the Vilenkin Groups on the Interval [0,1) -- 1.4 Convex Functions and Classical Inequalities -- 1.5 Lebesgue Spaces -- 1.6 Dirichlet Kernels -- 1.7 Lebesgue Constants -- 1.8 Vilenkin-Fourier Coefficients -- 1.9 Partial Sums -- 1.10 Final Comments and Open Questions -- 2 Martingales and Almost Everywhere Convergence of Partial Sums of Vilenkin-Fourier Series -- 2.1 Introduction -- 2.2 Conditional Expectation Operators -- 2.3 Martingales and Maximal Functions -- 2.4 Calderon-Zygmund Decomposition -- 2.5 Almost Everywhere Convergence of Vilenkin-Fourier Series -- 2.6 Almost Everywhere Divergence of Vilenkin-Fourier Series -- 2.7 Final Comments and Open Questions -- 3 Vilenkin-Fejér Means and an Approximate Identity in Lebesgue Spaces -- 3.1 Introduction -- 3.2 Vilenkin-Fejér Kernels -- 3.3 Approximation of Vilenkin-Fejér Means -- 3.4 Almost Everywhere Convergence of Vilenkin- Fejér Means -- 3.5 Approximate Identity -- 3.6 Final Comments and Open Questions -- 4 Nörlund and T Means of Vilenkin-Fourier Series in Lebesgue Spaces -- 4.1 Introduction -- 4.2 Well-Known and New Examples of Nörlund and TMeans -- 4.3 Regularity of Nörlund and T Means -- 4.4 Kernels of Nörlund Means -- 4.5 Kernels of T Means -- 4.6 Norm Convergence of Nörlund and T Means in Lebesgue Spaces -- 4.7 Almost Everywhere Convergence of Nörlund and T Means -- 4.8 Convergence of Nörlund and T Means in Vilenkin-Lebesgue Points -- 4.9 Riesz and Nörlund Logarithmic Kernels and Means -- 4.10 Final Comments and Open Questions -- 5 Theory of Martingale Hardy Spaces -- 5.1 Introduction -- 5.2 Martingale Hardy Spaces and Modulus of Continuity.
001451471 5058_ $$a9.7 Atomic Decomposition of Variable Hardy Spaces -- 9.8 Martingale Inequalities in Variable Spaces -- 9.9 Partial Sums of Vilenkin-Fourier Series in Variable Lebesgue Spaces -- 9.10 The Maximal Fejér Operator on Hp(·) -- 9.11 Final Comments and Open Questions -- 10 Appendix: Dyadic Group and Walsh and Kaczmarz Systems -- 10.1 Introduction -- 10.2 Walsh Group and Walsh and Kaczmarz Systems -- 10.3 Estimates of the Walsh-Fejér Kernels -- 10.4 Walsh-Fejér Means in Hp -- 10.5 Modulus of Continuity in Hp and Walsh-Fejér Means -- 10.6 Riesz and Nörlund Logarithmic Means in Hp -- 10.7 Maximal Operators of Kaczmarz-Fejér Means on Hp -- 10.8 Modulus of Continuity in Hp and Kaczmarz-Fejér Means -- 10.9 Final Comments and Open Questions -- References -- Notations -- Index.
001451471 506__ $$aAccess limited to authorized users.
001451471 520__ $$aThis book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.
001451471 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed December 19, 2022).
001451471 650_0 $$aFourier series.
001451471 650_0 $$aMartingales (Mathematics)
001451471 650_0 $$aHardy spaces.
001451471 655_0 $$aElectronic books.
001451471 7001_ $$aTephnadze, George,$$eauthor.
001451471 7001_ $$aWeisz, Ferenc,$$d1964-$$eauthor.$$1https://isni.org/isni/0000000122802512
001451471 77608 $$iPrint version: $$z3031144589$$z9783031144585$$w(OCoLC)1335115067
001451471 852__ $$bebk
001451471 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-14459-2$$zOnline Access$$91397441.1
001451471 909CO $$ooai:library.usi.edu:1451471$$pGLOBAL_SET
001451471 980__ $$aBIB
001451471 980__ $$aEBOOK
001451471 982__ $$aEbook
001451471 983__ $$aOnline
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