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

Bernhelm Booss-Bavnbek*, Chaofeng Zhu, Alessandro Portaluri, Yihan Ji

*Corresponding author

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningpeer review

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.
OriginalsprogEngelsk
TitelTrails in Modern Theoretical and Mathematical Physics : A Volume in Tribute to Giovanni Morchio
RedaktørerAndrea Cintio, Alessandro Michelangeli
Antal sider18
UdgivelsesstedCham
ForlagSpringer Nature Switzerland AG
Publikationsdatodec. 2023
Sider53-70
ISBN (Trykt)978-3-031-44987-1, 978-3-031-44990-1
ISBN (Elektronisk)978-3-031-44988-8
DOI
StatusUdgivet - dec. 2023

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