The Structure of Functions - Monographs in Mathematics - Hans Triebel - Livros - Springer Basel - 9783034894944 - 1 de novembro de 2012
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The Structure of Functions - Monographs in Mathematics Softcover reprint of the original 1st ed. 2001 edition

Hans Triebel

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The Structure of Functions - Monographs in Mathematics Softcover reprint of the original 1st ed. 2001 edition

This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier­ strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m) : m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N~. One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . ~m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . ~m E C. This resembles, at least formally, the Weier­ strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces.


425 pages, 5 black & white illustrations, biography

Mídia Livros     Paperback Book   (Livro de capa flexível e brochura)
Lançado 1 de novembro de 2012
ISBN13 9783034894944
Editoras Springer Basel
Páginas 425
Dimensões 178 × 254 × 23 mm   ·   757 g
Idioma English  

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