Advanced course of mathematical analysis 3

Juan M. Delgado Sanchez, Tomas Dominguez Benavides9812818448, 9789812818447

This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of the present-day research in different areas of mathematical analysis (complex variable, harmonic analysis, real analysis and functional analysis) that holds great promise for current and future developments. These review articles are highly useful for those who want to learn about these topics, as many results scattered in the literature are reflected through the many separate papers featured herein.

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Table of contents :
CONTENTS……Page 14
PREFACE……Page 8
ORGANIZING COMMITTEES……Page 12
1. Introduction……Page 16
2. Hyperbolic dynamics……Page 19
3. Superattracting dynamics……Page 23
4. Parabolic dynamics……Page 24
5. Elliptic dynamics……Page 35
References……Page 41
1. Notation and preliminaries……Page 43
2. Methods and applications……Page 46
References……Page 52
1. Discrete translates, generating functions……Page 54
2. Connections with density of exponentials……Page 55
3. The problem in L1(R) and its connections with the spectral radious problem……Page 56
4. Relation with quasianalytic classes……Page 58
5. The spectral sets for L1(R)……Page 59
6. The generators for L1(R)……Page 60
7. The restricted problem……Page 62
References……Page 63
1. Introduction……Page 64
2. Distance to spaces of continuous functions……Page 67
3. Distances to spaces of continuous functions on compact spaces……Page 69
4. Distance to Banach spaces……Page 71
5. Distances to continuous functions on countably K-determined spaces……Page 75
6. Baire one functions……Page 77
7. Further studies……Page 79
References……Page 80
1. Fractional integration……Page 82
2. Functions with controlled mean oscillation……Page 90
3. Smooth function spaces and wavelets……Page 94
References……Page 100
Domination by positive operators and strict singularity F. L. Hern andez……Page 101
1. Strictly singular operators……Page 102
2. Strictly singular inclusions……Page 103
3. Domination by strictly singular operators……Page 105
4. Powers of dominated operators……Page 108
References……Page 110
The Banach space Lp E. Odell……Page 126
1. Introduction……Page 112
2. The origin of the Hahn{Banach Theorem……Page 113
3. Helly……Page 115
4. The Landmark”: Helly’s 1921 article……Page 117
5. Helly’s technique……Page 119
7. Intersection properties……Page 120
References……Page 123
References……Page 152
1. Continuous functions with dense orbits……Page 154
2. Some properties of hypercyclic operators……Page 156
3. Ansari’s theorem……Page 159
4. Variations on a theme of L eon{Saavedra and M uller……Page 161
5. Dual hypercyclic operators……Page 162
References……Page 208
1. Operator spaces and completely bounded maps……Page 169
2. The fundamental theorem and some consequences……Page 172
3. Tensor products of operator spaces……Page 173
4.1. An application of the operator{space projective tensor product……Page 177
4.2. An application to nonselfadjoint operator algebras……Page 178
5.1. An application to Fourier algebras……Page 179
5.2. An application of the Haagerup tensor product……Page 180
6. Applications to Probability Theory……Page 181
References……Page 184
1. Introduction……Page 185
2. Social equilibrium……Page 187
3. From social equilibrium to competitive equilibrium……Page 190
4. Equilibrium and effciency……Page 194
5. Final comments……Page 196
References……Page 197
2. Prerequisities……Page 199
3. Basic properties of F-algebras……Page 203
4. Ideals in F-algebras……Page 204