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Anotace knihy

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.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics Calculus & mathematical analysis

• Plný název: Structure of Functions
• Autor: Hans Triebel
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 425
• EAN: 9783034894944
• ISBN: 3034894945
• ID: 06798695
• Nakladatelství: Springer Basel
• Hmotnost: 832 g
• Rozměry: 254 × 178 × 24 mm
• Datum vydání: 01. November 2012

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