Theory of p adic distributions albeverio s khrennikov a yu shelkovich v m
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Other important contributions concern and of infinite dimensional. Duration: 8 hours 6 theoretical and 2 practical. For some classes of hyperbolic systems of conservation laws in several space dimension, too we introduce the definitions of a δ-shock wave type solution relevant to the front problem. Zelenov, p-Adic Analysis and Mathematical Physics World Scientific, Sin- gapore, 1994. We construct the -adic Colombeau-Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. In asense, this result was unexpected. Laugwitz, Anwendungen unendlicher kleiner Zahlen: I.

Piatetskii-Shapiro, Generalized Functions, Representation Theory and Automorphic Functions Vol. We introduce the adelic Lizorkin spaces of test functions and distributions and give the characterization of these spaces in terms of adelic wavelet functions. It is proved that the mass, momentum and energy transport processes between the area outside the of one-dimensional δ-shock wave front and this front are going on such that the total mass, momentum and energy are independent of time, while the mass and energy concentration processes onto the moving δ-shock wave front are going on. Unlike the Colombeau algebra, whose elements have no explicit functional interpretation, elements of the algebra are infinite-dimensional Schwartz vector-valued distributions. Albeverio is Professor in the Faculty of Mathematics and Natural Sciences at the University of Bonn, Germany. We use the notation and results of classical book 13.

This system has been used to describe the formation of large-scale structures of the universe. We prove - 0 -shock balance relations connected with area transportation. The connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators is studied. Some problems of spectral analysis of pseudo-differential operators are studied. We study the spectral properties of the fractional operator introduced by S. The point value of a generalized function from Gp Qnp is well defined Subsec. We shall write this fact using the notation f g.

Talagrand: Lectures in Probability and Statistics. Moreover, it has some additionalgood properties. Shelkovich, Colombeau generalized functions: a theory based on harmonic regularizations, Mat. I: A Volume in Honor of Sergio Albeverio. In contrast to real wavelets, p-adic wavelets are related to the group representation theory; namely, the frames of p-adic wavelets are the orbits of p-adic transformation groups systems of coherent states. The algebraic aspect of singular solutions δ -shocks to systems of conservation laws is studied. The theory of p-adic wavelets; 9.

Lectures from the 30th Summer School in Probability Theory held in Saint-Flour, 2000. We construct some versions of the Colombeau theory. This norm is defined as follows. Its extended introduction and self-contained presentation also make it accessible to graduate students approaching the theory for the first time. Distributional asymptotics and p-adic Tauberian theorems; 13. As far as we know, exact S-shock wave type solutions for the first system have never been constructed. We prove that the nonlinear flux-functions for δ-shock solutions are well defined Schwartz distributions, and describe their singularities.

This book presents, for the first time in print, a complete account of Harish-Chandra's original lectures on this subject, including his extension and proof of Howe's Theorem. The products of distributions are continuous linear functionals. Member of the since its foundation 2006. Lectures given at the C. Balance re- lations connected with area transportation, in particular, mass and momen- tum transportation relations for the zero-pressure gas dynamics system, are derived.

We study the propagation of δ-shocks in two hyperbolic systems of conservation laws. For these operators wavelets were not eigenvectors, but matrices of operators in wavelet bases have non-zero matrix elements only for finite number of main diagonals. Steklova, 245 2004 , 29—40 ; Proc. The sequential theories of multiplication of distributions were constructed in the papers of Ya. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling. Proof of a theorem on weak asymptotic expansions; D. Suppose {fk x } Np Qnp.

Here and in what follows dnx denotes the improper integral Qnp dx. One-dimensional and multidimensional wavelet bases and their relation to the spectral theory of pseudodifferential operators are discussed. The aim of this paper is to explain how to derive integral identities for defining δ-shock type solutions in the sense of Schwartzian distributions. Shelkovich, Propagation and interaction of delta-shock waves of a hyperbolic system of con-servation laws, in: Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the Ninth International Con-ference on Hyperbolic Problems held in CalTech, Pasadena, March 2529, 2002, edited by Thomas Y. We derive a criterion for a multidimensional p-adic wavelet function to be an eigenfunction for a pseudo-differential operator and prove that our wavelets are eigenfunctions of the fractional operator. Acknowledgements The first and third authors A. Contents:Analysis on the Field p-Adic Numbers:The Field of p-Adic NumbersAnalytic FunctionsAdditive and Multiplicative CharactersIntegration TheoryThe Gaussian IntegralsGeneralized FunctionsConvolution and the Fourier TransformationHomogeneous Generalized FunctionsPseudo-Differential Operators on the Field of p-Adic Numbers:The Operator D? Solutions of Cauchy problems are constructed for some typical systems of conservation laws.

Moreover, the embedding D Qnp Gp Qnp is an algebrahomomorphism, and the space D Qnp is a subalgebra of the Colombeau-Egorov algebra. Any researcher working with applications of p-adic analysis will find much of interest in this book. . It is so-called - n -shock wave, where - n is n-th derivative of the delta function. In order to define them, some special integral identities are introduced which extend the concept of weak solution, and the Rankine-Hugoniot conditions are derived. The norm of Qp satisfies the strong triangle inequality x + y p max x p, y p. The algebra Gp Qnp of generalized functions f is associative and commutative.

Duration: 8 hours 6 theoretical and 2 practical. He grew up in Lugano, Switzerland. Khrennikov is Professor of Applied Mathematics and Director of the International Center for Mathematical Modeling in Physics, Engineering and Cognitive Sciences at Vaxjoe University, Sweden. Denote by E Qp and D Qp the linear spaces of locally-constant C-valued functions on Qp and locally- constant C-valued functions with compact support so-called test functions , respectively. The basic idea of this characterization is to introduce an analogue to nonstandard num-bers.