Search

Your search keyword '"11F85, 42C40, 47G30 (Primary)"' showing total 2 results
Start Over Descriptor "11F85, 42C40, 47G30 (Primary)"
2 results on '"11F85, 42C40, 47G30 (Primary)"'

1. Non-Haar $p$-adic wavelets and their application to pseudo-differential operators and equations

Author

Khrennikov, A. Yu. and Shelkovich, V. M.

Subjects
Mathematical Physics, Mathematics - General Mathematics, 11F85, 42C40, 47G30 (Primary), 26A33, 46F10 (Secondary)
Abstract

In this paper a countable family of new compactly supported {\em non-Haar} $p$-adic wavelet bases in ${\cL}^2(\bQ_p^n)$ is constructed. We use the wavelet bases in the following applications: in the theory of $p$-adic pseudo-differential operators and equations. Namely, we study the connections between wavelet analysis and spectral analysis of $p$-adic pseudo-differential operators. A criterion for a multidimensional $p$-adic wavelet to be an eigenfunction for a pseudo-differential operator is derived. We prove that these wavelets are eigenfunctions of the fractional operator. In addition, $p$-adic wavelets are used to construct solutions of linear and semi-linear pseudo-differential equations. Since many $p$-adic models use pseudo-differential operators (fractional operator), these results can be intensively used in these models.

Published
2008

2. Non-Haar p-adic wavelets and their application to pseudo-differential operators and equations

Author

V. M. Shelkovich and A. Yu. Khrennikov

Subjects
Pure mathematics, Mathematics::Number Theory, FOS: Physical sciences, Haar, p-Adic compactly supported wavelet bases, p-Adic Lizorkin spaces, Operator (computer programming), Wavelet, Fractional operators, General Mathematics (math.GM), 26A33, 46F10 (Secondary), FOS: Mathematics, Order (group theory), Spectral analysis, Mathematics - General Mathematics, Mathematical Physics, Mathematics, Applied Mathematics, 11F85, 42C40, 47G30 (Primary), Mathematical Physics (math-ph), Function (mathematics), Eigenfunction, Differential operator, p-Adic pseudo-differential equations, p-Adic pseudo-differential operators
Abstract

In the present paper an infinite family of new compactly supported non-Haar p-adic wavelet bases in L 2 ( Q p n ) is constructed. These bases cannot be constructed in the framework of any of known theories. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. The connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators is studied. 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. p-Adic wavelets are used to construct solutions of linear (the first and second order in t) and semi-linear evolutionary pseudo-differential equations. Since many p-adic models use pseudo-differential operators (fractional operator), our results can be intensively used in these models.

Published
2010

Catalog

Books, media, physical & digital resources
See catalog results