Harmonic Analysis and the Theory of Probability (Dover Books on Mathematics)

Book Details

• Author: Salomon Bochner

• Publisher: Dover

• Binding: Paperback

• Format: Import

• Number of Pages: 192

• Release Date: 27-08-2005

• ISBN: 9780486446202

• Package Dimensions: 8.5 x 5.4 x 0.6 inches

• Languages: English

About the Book

In this classic volume, Salomon Bochner explores the intersection of harmonic analysis and probability theory. Initially published in 1955, the book reflects Bochner's shift toward a more probabilistic perspective on harmonic analysis. The work is deeply rooted in the legacy of Joseph Fourier and P.S. Laplace, whose studies of heat theory and probability, respectively, laid the foundation for much of the development in harmonic analysis.

The book covers essential topics such as:

• Fourier Series and Integrals in Multiple Variables

• The Bochner Integral

• Transforms of Plancherel, Laplace, Poisson, and Mellin

• Applications to Boundary Value Problems and Dirichlet Series

• Bessel Functions and Completely Monotone Functions

In particular, the last two chapters introduce Bochner's characteristic functional, a key concept that connects Fourier transforms with Euclidean-like spaces of infinitely many dimensions. This concept is crucial in the study of stochastic processes and plays a role analogous to that of Fourier transforms in the analysis of numerical random variables.

This volume is especially valuable for advanced students and researchers in probability theory, mathematical analysis, and stochastic processes, offering both theoretical insights and practical applications in a variety of fields including boundary value problems and random variables.

About the Author

Salomon Bochner was a prominent mathematician known for his contributions to harmonic analysis and probability theory. His work, especially during the 1930s and 40s, had a profound impact on the development of Fourier analysis and its applications to stochastic processes. Bochner's exploration of the Bochner integral and the characteristic functional remains influential in both mathematics and its applied fields.