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 $D^{\alpha }+{\sum }_{i,j=1}^n{b}_{ij}<{\delta }_{x_j},\cdot >{\delta }_{x_i}$ in a form that is maximally adapted for the preservation of physically meaningful relations to the parameters $b_{ij}$ of the singular potential.

12 pages

Cited by in corpus (2)

• p-Adic Schrödinger-Type Operator with Point Interactions
• From Reference Frame Relativity to Relativity of Mathematical Models : Relativity Formulas in a Variety of Non-Archimedean Setups