p-Adic Fractional Differentiation Operator with Point Interactions

Details p-Adic Fractional Differentiation Operator with Point Interactions p-Adic Fractional Differentiation Operator with Point Interactions

2006-12-19

arxiv.org/abs/math-ph/0612061v1

Physics

Mathematical Physics

12 pages

Scientific paper

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.

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