The Dichotomy of Forms and Operators and the Role of Green’s Forms

Bernhelm Booß-Bavnbek; Yihan Ji; Alessandro Portaluri; Chaofeng Zhu

doi:10.1007/9783031449888_5

The Dichotomy of Forms and Operators and the Role of Green’s Forms

Bernhelm Booß-Bavnbek, Yihan Ji, Alessandro Portaluri, Chaofeng Zhu

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We consider a sesquilinear form on sections of a Hermitian bundle over a (not necessarily compact) smooth Riemannian manifold with boundary. We assume that in local coordinates, the form can be written as the integral of the inner product of differential expressions of the sections. We assign a linear operator to the form and show that it is a uniquely determined differential operator. We prove the existence and uniqueness of a differential operator on the boundary which makes a variant of Green’s formula hold.

Original language	English (US)
Title of host publication	Trails in Modern Theoretical and Mathematical Physics
Subtitle of host publication	a Volume in Tribute to Giovanni Morchio
Publisher	Springer International Publishing
Pages	53-70
Number of pages	18
ISBN (Electronic)	9783031449888
ISBN (Print)	9783031449871
DOIs	https://doi.org/10.1007/9783031449888_5
State	Published - Jan 1 2023

ASJC Scopus subject areas

General Physics and Astronomy

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10.1007/9783031449888_5

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AU - Portaluri, Alessandro

AU - Zhu, Chaofeng

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N2 - We consider a sesquilinear form on sections of a Hermitian bundle over a (not necessarily compact) smooth Riemannian manifold with boundary. We assume that in local coordinates, the form can be written as the integral of the inner product of differential expressions of the sections. We assign a linear operator to the form and show that it is a uniquely determined differential operator. We prove the existence and uniqueness of a differential operator on the boundary which makes a variant of Green’s formula hold.

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The Dichotomy of Forms and Operators and the Role of Green’s Forms

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