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Complete Systems of Eigenfunctions of the Vladimirov Operator in L2(Br) and L2(ℚp).
- Source :
-
Journal of Mathematical Sciences . Mar2019, Vol. 237 Issue 3, p362-374. 13p. - Publication Year :
- 2019
-
Abstract
- We construct new bases of real functions from L2(Br) and from L2(ℚp). These functions are eigenfunctions of the p-adic pseudo-differential Vladimirov operator, which is defined on a compact set Br ⊂ ℚp of the field of p-adic numbers ℚp or, respectively, on the entire field ℚp. A relation between the basis of functions from L2(ℚp) and the basis of p-adic wavelets from L2(ℚp) is found. As an application, we consider the solution of the Cauchy problem with the initial condition on a compact set for a pseudo-differential equation with a general pseudo-differential operator that is diagonal in the basis constructed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 237
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 135148902
- Full Text :
- https://doi.org/10.1007/s10958-019-04163-7