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# $p$-Adic fractional differentiation operator with point interactions

### Abstract

Finite rank point perturbations of the $p$-adic fractional differentiation operator $D^{\alpha}$ are studied. The main attention is paid to the description of operator realizations (in $L_2(\mathbb{Q}_p)$) of the heuristic expression $D^{\alpha}+\sum_{i,j=1}^{n}b_{ij}\delta_{x_i}$ in a form that is maximally adapted for the preservation of physically meaningful relations to the parameters $b_{ij}$ of the singular potential.

### Article Information

 Title $p$-Adic fractional differentiation operator with point interactions Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 169-180 MathSciNet MR2336719 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

S. Kuzhel
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

S. Torba
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

S. Kuzhel
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

S. Kuzhel and S. Torba, $p$-Adic fractional differentiation operator with point interactions, Methods Funct. Anal. Topology 13 (2007), no. 2, 169-180.

### BibTex

@article {MFAT400,
AUTHOR = {Kuzhel, S. and Torba, S.},
TITLE = {$p$-Adic fractional differentiation operator with point interactions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {2},
PAGES = {169-180},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=400},
}