Theory of p-adic Distributions
Theory of <I>p</I>-adic Distributions
A. Yu Khrennikov, Växjö Universitet, Sweden
V. M. Shelkovich, St Petersburg State University
$65.99
USDThis 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.
- Contains introductions to the theory of p-adic numbers, p-adic functions and p-adic distributions suitable for the non-specialist
- Contains many new results recently published in leading journals
- Self-contained presentation makes the book suitable for use in graduate courses
Product details
March 2010Paperback
9780521148566
368 pages
229 × 152 × 21 mm
0.54kg
Available
Table of Contents
- 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.
