Locally Self-adjoint Extensions of Nonlinear Smooth Operators and Abstract Boundary Conditions

TL;DR

This paper investigates smooth operators in real Hilbert spaces with symmetric derivatives, describing their locally self-adjoint extensions via abstract boundary conditions using symplectic differential geometry.

Contribution

It introduces a novel framework for characterizing locally self-adjoint extensions of nonlinear smooth operators through abstract boundary conditions.

Findings

Characterization of locally self-adjoint extensions

Application of symplectic differential geometry concepts

Framework for boundary condition analysis

Abstract

In a real Hilbert spaces H a smooth operator F is studied, whose derivative at each point of its domain is a symmetric operator. In terms of abstract boundary conditions locally self-adjoint extensions of this operator are described. We use some concepts and facts from symplectic differential geometry.