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Titlebook: Suprematism in Harmonic Analysis; Antonio Córdoba Book 2024 The Editor(s) (if applicable) and The Author(s), under exclusive license to Sp

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发表于 2025-3-21 18:00:53 | 显示全部楼层 |阅读模式
书目名称Suprematism in Harmonic Analysis
编辑Antonio Córdoba
视频videohttp://file.papertrans.cn/886/885293/885293.mp4
概述Winner of the Ferran Sunyer i Balaguer Prize for the best monograph 2024.Proves the Kakeya maximal function theorem.Offers an in-depth exploration of crucial topics in harmonic analysis
丛书名称Progress in Mathematics
图书封面Titlebook: Suprematism in Harmonic Analysis;  Antonio Córdoba Book 2024 The Editor(s) (if applicable) and The Author(s), under exclusive license to Sp
描述.This award-winning monograph explores advanced topics in harmonic analysis, addressing both classical and contemporary problems. Several connections to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a certain geometric point of view underlying proofs and arguments...The opening of the book is dedicated to a few results, with short statements and proofs, that could be called “mathematical haikus”. Then, in the first part of the book, singular integrals beyond the classical Calderón-Zygmund theory, such as Vitali-type covering lemmas and estimates for the corresponding maximal operators, are explored. The exponential overlapping of parallelepipeds, the strong maximal function, and Zygmund‘s conjecture about monotonic bases are also covered. The core of this part is devoted to the Kakeya maximal function and its relation to the spherical summation of Fourier series and integrals. The two-dimensional case is well understood, but the case of higher dimensions still presents many open problems and conjectures. The chapters in the second part of the book treat questions at the interface of harmonic analysis and number theory, including
出版日期Book 2024
关键词Harmonic analysis; Hilbert transforms; Euclidean space; Basicovitch sets; Kakeya maximal function theore
版次1
doihttps://doi.org/10.1007/978-3-031-73737-4
isbn_softcover978-3-031-73739-8
isbn_ebook978-3-031-73737-4Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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发表于 2025-3-21 22:25:29 | 显示全部楼层
发表于 2025-3-22 03:02:03 | 显示全部楼层
Encounters at the interface with number theory,they have been successfully applied also to a field in pure mathematics, namely number theory, and here it seems to be of importance precisely to consider those functions whose representability by trigonometric series has not been yet investigated”.
发表于 2025-3-22 05:56:26 | 显示全部楼层
Weyl sums and atomic energy oscillations,f first principles. It is a plausible goal having a distinguished history, but very difficult to achieve. And it rarely excites physicists, because what mathematicians can rigorously prove is not usually a hot topic for them.Nevertheless,we can always quote E.Wigner’s comment about the unreasonable
发表于 2025-3-22 12:35:51 | 显示全部楼层
Book 2024to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a certain geometric point of view underlying proofs and arguments...The opening of the book is dedicated to a few results, with short statements and proofs, that could be called “mathematical haiku
发表于 2025-3-22 15:15:29 | 显示全部楼层
0743-1643 ration of crucial topics in harmonic analysis.This award-winning monograph explores advanced topics in harmonic analysis, addressing both classical and contemporary problems. Several connections to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a
发表于 2025-3-22 19:36:10 | 显示全部楼层
All those rectangles,dy and Littlewood was based on the properties of rearrangements of measurable functions, and was expressed in the picturesque language of cricket. But it can also be obtained from elementary geometrical considerations.
发表于 2025-3-23 00:30:44 | 显示全部楼层
发表于 2025-3-23 04:25:49 | 显示全部楼层
Antonio Córdobaader may refer to [8, 58]..In the remainder of the book, we will assume that the reader is familiar with First Order Logic (FOL), Logic Programming (LP) and Prolog. A good introduction to LP is the book by Lloyd [154]; good introductions to Prolog are the books by Sterling and Shapiro [227] and by B
发表于 2025-3-23 06:48:16 | 显示全部楼层
Antonio Córdobaal time. The generalisation is such that refinement is compositional. This means that refinement at the individual level implies refinement at the multi-agent system level. Compositionality is an important property since it reduces heavily the verification process. Thus having a theory of refinement
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