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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.
| Autorius: | Hans Triebel |
| Serija: | Monographs in Mathematics |
| Leidėjas: | Birkhäuser Basel |
| Išleidimo metai: | 2012 |
| Knygos puslapių skaičius: | 440 |
| ISBN-10: | 3034894945 |
| ISBN-13: | 9783034894944 |
| Formatas: | 254 x 178 x 24 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „The Structure of Functions“
