| 书目名称 | Explorations in Harmonic Analysis | | 副标题 | With Applications to | | 编辑 | Steven G. Krantz | | 视频video | | | 概述 | Provides an introduction to a particular direction in modern harmonic analysis.Self-contained text on analysis of integral operators.Presents both fundamentals and applications of harmonic analysis, e | | 丛书名称 | Applied and Numerical Harmonic Analysis | | 图书封面 |  | | 描述 | Harmonic analysis is a venerable part of modern mathematics. Its roots began, perhaps, with late eighteenth-century discussions of the wave equation. Using the method of separation of variables, it was realized that the equation could be solved with a data function of the form?(x)= sin jx for j? Z.Itwasnaturaltoask, using the philosophy of superposition, whether the equation could then be solved with data on the interval [0,?] consisting of a nite linear combinationof the sin jx. With an af rmative answer to that question, one is led to ask about in?nite linear combinations. This was an interesting venue in which physical reasoning interacted with mathematical reasoning. Physical intuition certainly suggests that any continuous function? can be a data function for the wave equation. So one is led to ask whether any continuous? can be expressed as an (in nite) superposition of sine functions. Thus was born the fundamental question of Fourier series. No less an eminence gris than Leonhard Euler argued against the proposition. | | 出版日期 | Textbook 2009 | | 关键词 | Fourier analysis; Fourier transform; Singular integral; complex function theory; harmonic analysis; integ | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-8176-4669-1 | | isbn_ebook | 978-0-8176-4669-1Series ISSN 2296-5009 Series E-ISSN 2296-5017 | | issn_series | 2296-5009 | | copyright | Birkhäuser Boston 2009 |
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