Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
26.01.1947
E-mail: Keywords: nonselfadjoint operator; Friedrics' model; perturbation of continuous spectrum; spectral singularity; function of operator.
Subject:
Theorem on residue of the pseudoresolvent — analogy of known theorem about resolvent — is given.The minimal extension of the pseudoresolvent till resolvent is constructed, this construction is involved in spectral analysis of non-selfadjoint operators. The main subject is Friedrichs' model which permet to consider the Sturm–Liouville's operators too. For abstracts operators of this model the notion of maximal operators and formula of separation of branchement (closed no Sohotsky formula) are introduced. On this base the construction of function of the operator (with spectral singularities) without exit from space is given. As applications one can, for exemple, prove finitness of point spectrum nearly of extrems of continuous spectrum and obtain the terms in asymptotic behaviour of the solution of evolution equation, generic by spectral singularities of the operator. In this case one can consider nonlocal perturbation both the action and the boundary condition of Sturm–Liouville's operator.
Main publications:
On normal eigenvalue embedded in continuous spectrum // Meth. Funct. Anal. and Topology, 2001, 1, 1–16.
