Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\"odinger Operators on Bounded Lipschitz Domains

TL;DR

This paper investigates Robin-to-Robin maps and Krein-type resolvent formulas for Schrödinger operators with generalized Robin boundary conditions on bounded Lipschitz domains, advancing the mathematical understanding of boundary value problems.

Contribution

It introduces new Krein-type resolvent formulas and analyzes Robin-to-Robin maps for Schrödinger operators on Lipschitz domains, extending existing theories to more general boundary conditions.

Findings

Derived explicit Krein-type resolvent formulas

Analyzed properties of Robin-to-Robin maps on Lipschitz domains

Extended boundary value problem solutions to generalized Robin conditions

Abstract

We study Robin-to-Robin maps, and Krein-type resolvent formulas for Schr\"odinger operators on bounded Lipschitz domains in $\bbR^n$, $n\ge 2$, with generalized Robin boundary conditions.