# Functional model for boundary-value problems

## TL;DR

This paper introduces a functional model for boundary-value problem operators, offering explicit resolvent formulas via Dirichlet-to-Neumann maps, aiding spectral and parameter-dependent analysis.

## Contribution

It provides a novel functional model and explicit resolvent formulas for operators in boundary-value problems, enhancing spectral analysis capabilities.

## Key findings

- Explicit resolvent formulas derived for boundary-value operators
- Application of Dirichlet-to-Neumann maps in spectral analysis
- Facilitation of parameter-dependent problem analysis

## Abstract

We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of the associated generalised Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems as well as in the study of their spectra.