The method of equivalent operators in the study of one class of first-order differential operators with constant operator coefficient

A. G. Baskakov^a, G. V. Garkavenko^a, L. N. Kostina^a, N. B. Uskova<sup>b

a</sup> Voronezh State University
^b Voronezh State Technical University

Abstract: In this paper, we consider the application of the method of equivalent operators to the differential operator $\mathcal{L}=-d/dt+A: D(\mathcal{L})\subset\mathcal{F}\to\mathcal{F}$ acting in a homogeneous space of functions $\mathcal{F}$. We assume that the operator $A: D(A)\subset\mathcal{H}\to\mathcal{H}$ is a normal operator with compact resolvent in the Hilbert space $\mathcal{H}$. Conditions for its invertibility and estimates for the norm of the inverse in various spaces $\mathcal{F}$ are given.

Keywords: method of equivalent operators, operator with compact resolvent, Hilbert space, spectrum

UDC: 517.9

MSC: 47A75, 47B25, 47B36

DOI: 10.36535/2782-4438-2025-242-11-21