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math.FA2020
Locally Self-adjoint Extensions of Nonlinear Smooth Operators and Abstract Boundary Conditions
Leonid Zelenko
In a real Hilbert spaces H a smooth operator F is studied, whose derivative at each point of its domain is a symmetric operator. In terms of abstract boundary conditions locally se…
math.SP2020
Criterion of holomorphy with respect to a coupling constant of continuous functions of a perturbed self-adjoint operator
Leonid Zelenko
Sufficient and necessary conditions on the spectral measure of a self-adjoint operator , acting in a Hilbert space, are obtained, under which for any continuous scalar function…
math.SP2020
Conditions for discreteness of the spectrum to Schrödinger operator via non-increasing rearrangement, Lagrangian relaxation and perturbations
Leonid Zelenko
This work is a continuation of our previos paper, where for the Schrödinger operator $H=-Δ+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in the space , some sufficient c…