Learn the basics of white noise theory with White Noise Distribution Theory. This book covers the mathematical foundation and key applications of white noise theory without requiring advanced knowledge in this area. This instructive text specifically focuses on relevant application topics such as integral kernel operators, Fourier transforms, Laplacian operators, white noise integration, Feynman integrals, and positive generalized functions. Extremely well-written by one of the field's leading researchers, White Noise Distribution Theory is destined to become the definitive introductory resource on this challenging topic.
Table of Contents
Introduction to White Noise. Background. White Noise as an Infinite Dimensional Calculus. Constructions of Test and Generalized Functions. The S-Transform. Continuous Versions and Analytic Extensions. Delta Functions. Characterization Theorems. Differential Operators. Integral Kernel Operators. Fourier Transforms. Laplacian Operators. White Noise Integration. Feynman Integrals. Positive Generalized Functions. Appendix A: Notes and Comments. Appendix B: Miscellaneous Formulas.