Potentials of zero radius and Carleman operators
Let \(\Omega\) be an open subset of \(\mathbb{R}^\nu\); \(H_0\) is a selfadjoint operator in \(L^2(\Omega)\), and \(A\) is a subset of \(\Omega\) satisfying the uniform discreteness condition \[ d(A)\equiv \inf\{| \alpha-\beta|: \alpha,\beta\in A,\;\alpha\neq\beta\}> 0. \] Let \(D(H_0)\) be the domain of \(H_0\), \[ D_A= \{\varphi\in D(H_0): \varphi(\alpha)=0\;\forall\alpha\in A\}. \] An unconditional basis in the defect subspace of the operator \(H_0| D_A\) and the Green function for the selfadjoint extension of its closure are constructed.
scientific article; zbMATH DE number 923539
scientific article