Theory of p-adic Distributions
Linear and Nonlinear Models

A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.

S. Albeverio (Author), A. Yu Khrennikov (Author), V. M. Shelkovich (Author)

9780521148566, Cambridge University Press

Paperback, published 18 March 2010

368 pages
22.9 x 15.2 x 2.1 cm, 0.54 kg

"... constitutes a relevant contribution to the study of wavelets and multiresolution analysis, as well as to the study of linear and semilinear evolution equations via wavelets, in a p-adic setting." W.A. Zuniga Galindo, Mathematical Reviews

This 2010 book was the first devoted to the theory of p-adic wavelets and pseudo-differential equations in the framework of distribution theory. This relatively recent theory has become increasingly important in the last decade with exciting applications in a variety of fields, including biology, image analysis, psychology, and information science. p-Adic mathematical physics also plays an important role in quantum mechanics and quantum field theory, the theory of strings, quantum gravity and cosmology, and solid state physics. The authors include many new results, some of which constitute new areas in p-adic analysis related to the theory of distributions, such as wavelet theory, the theory of pseudo-differential operators and equations, asymptotic methods, and harmonic analysis. Any researcher working with applications of p-adic analysis will find much of interest in this book. Its extended introduction and self-contained presentation also make it accessible to graduate students approaching the theory for the first time.

Preface
1. p-Adic numbers
2. p-Adic functions
3. p-Adic integration theory
4. p-Adic distributions
5. Some results from p-adic L- and L- theories
6. The theory of associated and quasi associated homogeneous p-adic distributions
7. p-Adic Lizorkin spaces of test functions and distributions
8. The theory of p-adic wavelets
9. Pseudo-differential operators on the p-adic Lizorkin spaces
10. Pseudo-differential equations
11. p-Adic Schrödinger-type operator with point interactions
12. Distributional asymptotics and p-adic Tauberian theorems
13. Asymptotics of the p-adic singular Fourier integrals
14. Nonlinear theories of p-adic generalized functions
A. The theory of associated and quasi associated homogeneous real distributions
B. Two identities
C. Proof of a theorem on weak asymptotic expansions
D. One 'natural' way to introduce a measure on Q
References
Index.

Subject Areas: Calculus & mathematical analysis [PBK]