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$p$-Adic fractional differentiation operator with point interactions

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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.


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Article Information

Title$p$-Adic fractional differentiation operator with point interactions
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 169-180
MathSciNet MR2336719
CopyrightThe 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},
}


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