Analogs of generalized resolvents and eigenfunction expansions of relations generated by pair of differential operator expressions one of which depends on spectral parameter in nonlinear manner

TL;DR

This paper constructs analogs of generalized resolvents as integro-differential operators for relations generated by pairs of differential operator expressions, one depending nonlinearly on the spectral parameter, and derives eigenfunction expansions.

Contribution

It introduces a novel approach to construct generalized resolvents for differential relations with nonlinear spectral dependence and derives their eigenfunction expansions.

Findings

Constructed analogs of generalized resolvents as integro-differential operators.

Derived eigenfunction expansions for the relations.

Extended the theory to relations with nonlinear spectral parameter dependence.

Abstract

For the relations generated by pair of differential operator expressions one of which depends on the spectral parameter in the Nevanlinna manner we construct analogs of the generalized resolvents which are integro-differential operators. The expansions in eigenfunctions of these relations are obtained.