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Titlebook: Convergence and Summability of Fourier Transforms and Hardy Spaces; Ferenc Weisz Book 2017 Springer International Publishing AG 2017 Fejér

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發(fā)表于 2025-3-21 16:31:57 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Convergence and Summability of Fourier Transforms and Hardy Spaces
編輯Ferenc Weisz
視頻videohttp://file.papertrans.cn/238/237743/237743.mp4
概述Explores comprehensively the summability of Fourier transforms as well as the theory of Hardy spaces.Gathers classical results as well as recent results from the past 20-30 years.Considers strong summ
叢書名稱Applied and Numerical Harmonic Analysis
圖書封面Titlebook: Convergence and Summability of Fourier Transforms and Hardy Spaces;  Ferenc Weisz Book 2017 Springer International Publishing AG 2017 Fejér
描述This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations.?.Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike..
出版日期Book 2017
關(guān)鍵詞Fejér summability; fourier analysis; hardy spaces; Lebesgue points; strong summability; harmonic analysis
版次1
doihttps://doi.org/10.1007/978-3-319-56814-0
isbn_softcover978-3-319-86008-4
isbn_ebook978-3-319-56814-0Series ISSN 2296-5009 Series E-ISSN 2296-5017
issn_series 2296-5009
copyrightSpringer International Publishing AG 2017
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 23:14:14 | 只看該作者
One-Dimensional Fourier TransformsIn the first two sections, we introduce the Fourier transform for Schwartz functions and we extend it to ., ., . functions as well as to tempered distributions. We prove some elementary properties and the inversion formula. In Sect.?2.4, we deal with the convergence of Dirichlet integrals. Using som
板凳
發(fā)表于 2025-3-22 01:40:06 | 只看該作者
Multi-Dimensional Hardy Spacesngst others, inequalities, atomic decompositions, interpolation theorems, boundedness results are proved for these spaces. Basically, the results for . are very similar to those for the one-dimensional . spaces studied in Chap.?., so we omit the corresponding proofs. However, the proofs for . are di
地板
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Convergence and Summability of Fourier Transforms and Hardy Spaces
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2296-5009 “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike..978-3-319-86008-4978-3-319-56814-0Series ISSN 2296-5009 Series E-ISSN 2296-5017
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發(fā)表于 2025-3-23 03:33:10 | 只看該作者
https://doi.org/10.1007/979-8-8688-0500-4ost everywhere convergence. In Sect.?5.4, the convergence at Lebesgue points is investigated. Since the proofs are very different for different .’s, therefore each case needs new ideas. Using the result of the ..-summability, in the last section we prove the one-dimensional strong summability results presented in Sect.?..
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