# An Axiomatic Approach to Function Spaces, Spectral Synthesis, and Luzin Approximation (Memoirs of the American Mathematical Society) ebook

## by Yuri Netrusov,Lars Inge Hedberg

Memoirs of the American Mathematical Society 2007; 97 pp; MSC: Primary 46; Secondary 26; 31; 4. Lars Inge Hedberg; Yuri Netrusov

Memoirs of the American Mathematical Society 2007; 97 pp; MSC: Primary 46; Secondary 26; 31; 41. Electronic ISBN: 978-1-4704-0486-4 Product Code: MEMO/188/882. An Axiomatic Approach to Function Spaces, Spectral Synthesis, and Luzin Approximation. Lars Inge Hedberg; Yuri Netrusov. The authors define axiomatically a large class of function (or distribution) spaces on (N)-dimensional Euclidean space.

An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation. The main results of Chapter 1 characterize our spaces by means of local approximations, higher differences, and atomic representations. Lars Inge Hedberg and Yuri Netrusov. In Chapters 2 and 3 these results are applied to prove pointwise differentiability outside exceptional sets of zero capacity, an approximation property known as spectral synthesis, a generalization of Whitney's ideal theorem, and approximation theorems of Luzin (Lusin) type. View other years and numbers: Table of Contents.

by Lars Inge Hedberg, Lars Inge Hedberg, Yuri Netrusov. Published July 22, 2007 by Amer Mathematical Society. Function spaces, Approximation theory, Spectral synthesis (Mathematics), Functional analysis, Real analysis, Advanced, Mathematics, Science/Mathematics.

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Section . is devoted to an extension of the spectral synthesis theorem to Besov spaces of. . is devoted to an extension of the spectral synthesis theorem to Besov spaces of distributions. Chapter 3 is devoted to approximation theorems of Luzin type for the spaces studied in Chapter 1. In Section ., which is independent of the results of Sections . - ., we prove a theorem which improves earlier such results even in the case of Sobolev spaces. In part this result was announced by Netrusov in, but the proof has remained unpublished. This section is continued in Section . with an analogous theorem for spaces of distributions, which seems to be a question that has not been previously studied.

a metric space with measure Sobolev spaces the Luzin approximation. Netrusov, An Axiomatic Approach to Function Spaces, Spectral Synthesis, and Luzin Approximation, Memoirs of the Amer. Prokhorovich, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 5, pp. 55–66. Dedicated to the memory of Petr Lavrent’evich Ul’yanov.

Semantic Scholar extracted view of "An axiomatic approach to function spaces and . Approximation by Hölder Functions in Besov and Triebel–Lizorkin Spaces. Toni Heikkinen, Heli Tuominen.

Semantic Scholar extracted view of "An axiomatic approach to function spaces and spectral synthesis" by Lars Inge Hedberg. oceedings{Hedberg2003AnAA, title {An axiomatic approach to function spaces and spectral synthesis}, author {Lars Inge Hedberg}, year {2003} }. Lars Inge Hedberg. Mem am math SOC. In the original proof of the theorem on local approximation of functions by algebraic polynomials, Whitney estimated the deviation of the function from an interpolating polynomial with equally spaced nodes by means of finite differences.