Book: Characteristic Functions and Moment Sequences

Torben Maack Bisgaard and Zoltán Sasvári
Characteristic Functions and Moment Sequences.
Vol. I.
Nova Science, 2000.

Contents

1 Characteristic functions
  1.1 Notation and Preliminaries
  1.2 Definition, basic properties
  1.3 Inversion theorems
  1.4 Positive definiteness
  1.5 Convergence of positive definite and characteristic functions
  1.6 The theorems of Bochner and Plancherel
  1.7 The "discrete version" of the previous section
  1.8 Discrete distributions
  1.9 Pólya-type characteristic functions
  1.10 Differentiability
  1.11 Behaviour at infinity
  1.12 Analytic and entire characteristic functions
  1.13 Factorization theorems
  1.14 An important inequality
 
2 Moment sequences
  2.1 Moment sequences and positive definite sequences
  2.2 Determinacy
  2.3 Conditionally positive definite functions
  2.4 Orthogonal polynomials
 
A Auxiliary results from harmonic analysis
 
B Convergence of distribution functions
 
C Semi-definite matrices
 
Bibliography
 
Index
 
List of symbols