Topics in classical analysis and applications in honor of Daniel Waterman

CONTENTS......Page 8
Preface......Page 6
REMINISCENCES......Page 10
RESEARCH......Page 15
Reflexivity and Summability......Page 16
Harmonic Analysis......Page 17
Change of Variable......Page 18
Fourier Series and Generalized Variation......Page 19
Representation of Functions, Orthogonal Series......Page 21
Summability......Page 22
Papers......Page 23
DOCTORAL STUDENTS......Page 27
Reminiscences edited by L. Lardy, J. Troutman (with contributions by L. D’Antonio, G. T. Cargo, Ph. T. Church, D. Dezern, G. Gasper, P. Pierce, E. Poletsky, M. Schramm, F. Prus-Wisniowski, P. Schembari)......Page 28
1.1. Definitions......Page 40
1.2. Relating classes of operators......Page 41
1.3. A surprising connection......Page 44
1.5. Quantitative results for L2 concentration......Page 46
2.1. The early years......Page 48
2.2. On the virtues of procrastination......Page 49
3.1. A segue......Page 51
3.3. A conjecture about operators......Page 52
References......Page 53
Variants of a Selection Principle for Sequences of Regulated and Non-Regulated Functions V. V. Chistyakov, C. Maniscalco, Y. V. Tretyachenko......Page 54
1. Regulated Functions and Selection Principles......Page 55
2. Main Results......Page 58
3. Properties of N(ε, f, T) for Metric Space Valued Functions......Page 59
4. Functions with Values in a Metric Space: Proofs......Page 67
5. Functions with Values in a Metric Semigroup......Page 72
6. Functions with Values in a Re.exive Separable Banach Space......Page 77
References......Page 79
1. Introduction......Page 82
2. Preliminaries......Page 85
2.1. Four useful Lemmas......Page 87
3. Most of the Proofs......Page 91
References......Page 96
1. Introduction......Page 97
2. Uniform and Lp-Convergence......Page 98
3. Convergence Almost Everywhere: One-Dimensional Series......Page 101
4. Convergence Almost Everywhere: Multiple Series......Page 103
5. Concluding Remarks......Page 107
References......Page 109
1. Introduction......Page 111
2. Reality of the Zeros of the Functions Kiz(a) When a > 0......Page 113
3. Reality of the Zeros of the Functions Ξ(z) and Fa,c(z)......Page 115
Acknowledgment......Page 116
References......Page 117
1. Introduction......Page 119
2. Proofs......Page 122
References......Page 126
1. Introduction......Page 127
2. Spaces H2G......Page 131
2.1. A-invariant sets......Page 133
3.1. Definitions and Preliminary results......Page 136
3.2. Characterization of scaling functions of an H2G -FMRA and other cases......Page 139
4. On the Existence of H2G -MRA and H2G -FMRA......Page 146
References......Page 148
1. Introduction......Page 150
2. Representation Theorems......Page 155
3. Higher Order Cancellations......Page 159
4. Higher Order Commutators......Page 165
5. Comparison with Earlier Results and Some Questions......Page 166
References......Page 168
1. Introduction......Page 170
2. Greedy Approximation with Regard to the Trigonometric System......Page 172
References......Page 180
1. About the Definition......Page 182
2. Basic Properties......Page 185
3. The Structure of Regulated Functions......Page 188
4. Local Λ-Variation and Its Decomposition......Page 192
5. Continuity in Λ-Variation and Λ-Absolute Continuity......Page 194
6. Relationship Between ΛBV and ΛBVc......Page 196
References......Page 198
Author Index......Page 200