The Structure of Functions

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Springer Science & Business Media, 2001 - Mathematics - 425 pages
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This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations. The book is self-contained, although some parts may be considered as a continuation of the author's book "Fractals and Spectra" (MMA 91). It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated.
 

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Contents

II
1
III
10
IV
27
V
34
VI
41
VII
71
VIII
81
IX
101
XVIII
243
XIX
251
XX
253
XXI
294
XXII
310
XXIII
329
XXIV
348
XXV
355

X
120
XI
161
XII
167
XIII
181
XIV
202
XV
218
XVI
229
XVII
235
XXVI
357
XXVII
385
XXVIII
389
XXIX
403
XXX
419
XXXI
423
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