Format:
1 Online-Ressource (xvi, 351 pages)
,
digital, PDF file(s).
ISBN:
9781139107167
Series Statement:
London Mathematical Society lecture note series 370
Content:
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.
Content:
P-adic numbers -- P-adic functions -- P-adic integration theory -- P-adic distributions -- Some results from p-adic p-adic L-theories -- The theory of associated and quasi associated homogeneous p-adic distribution -- P-adic Lizorkin spaces of the test functions and distributions -- The theory of P-adic wavelets -- Pseudo-differential operators on the p-adic Lizorkin spaces -- Pseudo-differential equation -- A p-adic =Schrodinger-type operator with interactions -- Distributional asymptotic and p-adic Tauberian theorems -- Asymptotics of the p-adic singular Fourier integrals -- Nonlinear theories of p-adic generalized functions -- The theory of associated and quasi associated homogeneous real distributions -- Two identities -- Proof of a theorem on weak asymptotic expansions -- One natural way to introduce a measure on Qp
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521148566
Additional Edition:
ISBN 9780521148566
Additional Edition:
ISBN 9780521148566
Additional Edition:
Erscheint auch als Albeverio, Sergio, 1939 - Theory of p-adic distributions Cambridge [u.a.] : Cambridge University Press, 2010 ISBN 0521148561
Additional Edition:
ISBN 9780521148566
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521148566
Language:
English
Subjects:
Mathematics
Keywords:
p-adischer Zahlkörper
;
Funktionalanalysis
DOI:
10.1017/CBO9781139107167
Author information:
Khrennikov, Andrei 1958-
Author information:
Albeverio, Sergio 1939-
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