| The Structure of Functions Softcover Repri Edition Contributor(s): Triebel, Hans (Author) |
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ISBN: 3034894945 ISBN-13: 9783034894944 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: November 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Calculus - Medical - Mathematics | Differential Equations - General |
| Dewey: 515 |
| Series: Monographs in Mathematics |
| Physical Information: 0.89" H x 7" W x 10" (1.67 lbs) 425 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |