Introduction Quasi-analytic functions Szasz's theorem Certain integral expansions A class of singular integral equations Entire functions of the exponential type The closure of sets of complex exponential functions Non-harmonic Fourier series and a gap theorem Generalized harmonic analysis in the complex domain The harmonic analysis of random functions Bibliography Index.

"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

Fourier Transforms in the Complex Domain

The Fractal Geometry of Nature

* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit Theorems * Conditioning and Disintegration * Martingales and Optional Times * Markov Processes and Discrete-Time Chains * Random Walks and Renewal Theory * Stationary Processes and Ergodic Theory * Special Notions of Symmetry and Invariance * Poisson and Pure Jump-Type Markov Processes * Gaussian Processes and Brownian Motion * Skorohod Embedding and Invariance Principles * Independent Increments and Infinite Divisibility * Convergence of Random Processes, Measures, and Sets * Stochastic Integrals and Quadratic Variation * Continuous Martingales and Brownian Motion * Feller Processes and Semigroups * Ergodic Properties of Markov Processes * Stochastic Differential Equations and Martingale Problems * Local Time, Excursions, and Additive Functionals * One-Dimensional SDEs and Diffusions * Connections with PDEs and Potential Theory * Predictability, Compensation, and Excessive Functions * Semimartingales and General Stochastic Integration * Large Deviations * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices

http://cyber.sibsutis.ru:82/Monarev/docs/nauka/PROBABILITY/Kallenberg%20O.%20Foundations%20of%20Modern%20Probability%20(Springer,1997)(ISBN%200387949577)(535s).pdf

Foundations of modern probability

A class of nonharmonic Fourier series

1. Fourier series on T 2. The convergence of Fourier series 3. The conjugate function 4. Interpolation of linear operators 5. Lacunary series and quasi-analytic classes 6. Fourier transforms on the line 7. Fourier analysis on locally compact Abelian groups 8. Commutative Banach algebras A. Vector-valued functions B. Probabilistic methods.

/pdf/an-introduction-to-harmonic-analysis-5929oerr0v.pdf

An Introduction to Harmonic Analysis

(see, for example, Kaczmarz and Steinhaus [I, pp. 143-144]). Let (2.4) tap(t)} p = 1, 2, 3, be any orthonormal set of real functions, each belonging to L2(0, 1). Paley and 1 Wiener [II] have shown for each index p = 1, 2, that f ap(t) dx(t) exist as a generalized Stieltjes integral for almost all functions x(&) of C and that the equality W 1~~~~~~~~~~~~ |G a, ot(t) dx(t), * ,Iap(t) dx(t)] dwx (2.5) c 00 -p/2 L G(ui, * , up)euhu du, ... du.

https://www.jstor.org/stable/info/1969178

Fourier Transforms in the Complex Domain

Citations

The Fractal Geometry of Nature

Foundations of modern probability

A class of nonharmonic Fourier series

An Introduction to Harmonic Analysis

The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals

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