Eigenfunction expansions associated with operator differential equation depending on spectral parameter nonlinearly

TL;DR

This paper develops eigenfunction expansions for operator differential equations that depend nonlinearly on the spectral parameter in the Nevanlinna manner, advancing spectral theory methods.

Contribution

It introduces eigenfunction expansions for a class of operator differential equations with nonlinear spectral dependence, expanding the theoretical framework.

Findings

Eigenfunction expansions are established for the specified operator differential equations.

The approach handles nonlinear dependence on the spectral parameter in the Nevanlinna class.

The results extend classical spectral theory to more complex operator equations.

Abstract

For operator differential equation which depends on the spectral parameter in the Nevanlinna manner we obtain the expansions in eigenfunctions.