A Note on Operator-Theoretic Approach to Classic Boundary Value Problems for Harmonic and Analytic Functions in the Complex Plane Domain

TL;DR

This paper reformulates classical boundary value problems for harmonic and analytic functions in the complex plane using an operator-theoretic spectral framework, providing a unified abstract approach.

Contribution

It introduces an operator-theoretic formulation of classical boundary value problems, connecting them with spectral theory in a novel way.

Findings

Unified operator-theoretic framework for boundary value problems

Restatement of Poincare, Hilbert, and Riemann problems in spectral terms

Potential for new analytical and numerical methods

Abstract

The general spectral boundary value problem framework is utilized to restate boundary value problems of Poincare, Hilbert, and Riemann for harmonic and analytic functions in abstract operator-theoretic terms.