Spectral Properties of the Generator of a Semigroup Generated by the Volterra Integro-Differential Equation-Reference-Cited by-同舟云学术

Spectral Properties of the Generator of a Semigroup Generated by the Volterra Integro-Differential Equation

Published:2023-02-15 Issue:2 Volume:59 Page:275-279
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Vlasov V. V¹²,Rautian N. A¹²

Affiliation:

1. Lomonosov Moscow State University, Moscow, 119991, Russia

2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

Abstract

The spectral properties of a linear operator that is the generator of a semigroup generated by a Volterra integro-differential equation in a Hilbert space are studied. Such integro-differential equations can be implemented as partial integro-differential equations arising in the theory of viscoelasticity and the theory of heat propagation in media with memory and also have many other important applications.The established results on the Riesz basis property of the root vectors of the semigroup generator can be used in studying the properties of solutions of integro-differential equations.

Publisher

The Russian Academy of Sciences

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