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Item Details
| Title:
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THE STRUCTURE OF FUNCTIONS
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| By: |
Hans Triebel |
| Format: |
Paperback |
| List price:
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£69.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3034894945 |
| ISBN 13: |
9783034894944 |
| Publisher: |
SPRINGER BASEL |
| Pub. date: |
1 November, 2012 |
| Edition: |
Softcover reprint of the original 1st ed. 2001 |
| Series: |
Monographs in Mathematics 97 |
| Pages: |
437 |
| Synopsis: |
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. |
| Illustrations: |
5 black & white illustrations, biography |
| Publication: |
Switzerland |
| Imprint: |
Springer Basel |
| Returns: |
Returnable |
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