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Titlebook: Continuity, Integration and Fourier Theory; Adriaan C. Zaanen Textbook 1989 Springer-Verlag GmbH Germany, part of Springer Nature 1989 Ext

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書目名稱Continuity, Integration and Fourier Theory
編輯Adriaan C. Zaanen
視頻videohttp://file.papertrans.cn/237/236981/236981.mp4
叢書名稱Universitext
圖書封面Titlebook: Continuity, Integration and Fourier Theory;  Adriaan C. Zaanen Textbook 1989 Springer-Verlag GmbH Germany, part of Springer Nature 1989 Ext
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
關(guān)鍵詞Extension; Fourier series; Fourier transform; Hilbert space; differential equation; mathematical physics;
版次1
doihttps://doi.org/10.1007/978-3-642-73885-2
isbn_softcover978-3-540-50017-9
isbn_ebook978-3-642-73885-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag GmbH Germany, part of Springer Nature 1989
The information of publication is updating

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https://doi.org/10.1007/978-3-319-69886-1ormly by polynomials, i.e., for any ? > 0 there exists a polynomial P. such that |.(.)–. (.) | < ? holds for all . ∈ .. In other words, ||.–.|| < ?, where || ? || denotes the uniform norm in .(.). Equivaiently, we may say that there exists a sequence (. : n = 1,2,…) of polynomials such that ||.–.||
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https://doi.org/10.1007/978-3-319-69886-1. = 1 if . = . and . = 0 if . ≠ .. For our second definition, let (.: . = 0, ±1, ±2,...) be a set of real or complex functions, defined on the subset . of ?.. The set (.) is called an . (or .) on . if . is the complex conjugate of . and . stands for .… . Of course, the definition makes sense only if
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https://doi.org/10.1007/978-3-319-69886-1riants, one for sums and one for integrals. The original variant for integrals of continuous functions or Riemann integrable functions was extended to measurable functions without additional difficulties.
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Continuity, Integration and Fourier Theory978-3-642-73885-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
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