The Structure of Functions - Couverture souple

Triebel, Hans

Couverture souple

ISBN 10 : 3034894945 ISBN 13 : 9783034894944

Editeur : Birkhäuser, 2012

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.

A propos du livre

Présentation de l'éditeur

Dealing with the constructive Weierstrassian approach to the theory of function spaces and its various applications, this volume combines the advantages of atomic and wavelet representations to enhanced theories in spectral fractal elliptics and semi-linear equations.

Détails de l'édition

• Éditeur: Birkhäuser
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 3034894945
• ISBN 13: 9783034894944
• Reliure: Broché
• Nombre de pages: 440
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne