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Torba","submitted_at":"2007-03-27T14:58:41Z","abstract_excerpt":"A $p$-adic Schr\\\"{o}dinger-type operator $D^{\\alpha}+V_Y$ is studied. $D^{\\alpha}$ ($\\alpha>0$) is the operator of fractional differentiation and $V_Y=\\sum_{i,j=1}^nb_{ij}<\\delta_{x_j}, \\cdot>\\delta_{x_i}$ $(b_{ij}\\in\\mathbb{C})$ is a singular potential containing the Dirac delta functions $\\delta_{x}$ concentrated on points $\\{x_1,...,x_n\\}$ of the field of $p$-adic numbers $\\mathbb{Q}_p$. It is shown that such a problem is well-posed for $\\alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for $\\alpha>1$. 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