书目名称 | Continuity, Integration and Fourier Theory | 编辑 | Adriaan C. Zaanen | 视频video | http://file.papertrans.cn/237/236981/236981.mp4 | 丛书名称 | Universitext | 图书封面 |  | 描述 | This book is a textbook for graduate or advanced undergraduate students in mathematics and (or) mathematical physics. It is not primarily aimed, therefore, at specialists (or those who wish to become specialists) in integra tion theory, Fourier theory and harmonic analysis, although even for these there might be some points of interest in the book (such as for example the simple remarks in Section 15). At many universities the students do not yet get acquainted with Lebesgue integration in their first and second year (or sometimes only with the first principles of integration on the real line ). The Lebesgue integral, however, is indispensable for obtaining a familiarity with Fourier series and Fourier transforms on a higher level; more so than by us ing only the Riemann integral. Therefore, we have included a discussion of integration theory - brief but with complete proofs - for Lebesgue measure in Euclidean space as well as for abstract measures. We give some emphasis to subjectsof which an understanding is necessary for the Fourier theory in the later chapters. In view of the emphasis in modern mathematics curric ula on abstract subjects (algebraic geometry, algebraic topolo | 出版日期 | Textbook 1989 | 关键词 | Extension; Fourier series; Fourier transform; Hilbert space; differential equation; mathematical physics; | 版次 | 1 | doi | https://doi.org/10.1007/978-3-642-73885-2 | isbn_softcover | 978-3-540-50017-9 | isbn_ebook | 978-3-642-73885-2Series ISSN 0172-5939 Series E-ISSN 2191-6675 | issn_series | 0172-5939 | copyright | Springer-Verlag GmbH Germany, part of Springer Nature 1989 |
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