Boundary properties of the kernel of an elliptic pseudodifferential operator on a compact manifold with boundary
type: Item
instance of: scholarly article
title: Boundary properties of the kernel of an elliptic pseudodifferential operator on a compact manifold with boundary
zbMATH Open document ID: 0703.35183
DOI: 10.1007/BF00971490
author: Yu. E. Borovskij
published in: Siberian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let X be a smooth compact n-dimensional manifold with the boundary \(Y=\partial x\), \(X_ 0=int X\), E and F be complex vector bundles over X. Let A be an elliptic pseudo-differential operator of order m, \(P_ A\) be the orthoprojector on the Ker A in \(H^ 0(X,E)\) and \[ (P_ Af)(x)=\int_{X_ 0}P_ A(x,y)f(y)dy, \] so that \(P_ A(x,y)\) is the reproducing kernel in the Bergman-Aronszajn sense. Let \(P_ A(x)=tr P_ A(x,x)\). The author constructs the asymptotic expansion of \(P_ A(x)\) near the boundary Y. This expansion generalizes some results of S. Bergman and L. Hörmander.
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 35J50
zbMATH DE Number: 4153107
zbMATH Keywords: elliptic pseudo-differential operator
zbMATH Keywords: reproducing kernel
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: near the boundary
reviewed by: Yu V. Egorov
MaRDI profile type: Publication
cites work: Q3286588
cites work: \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
cites work: Boundary problems for pseudo-differential operators
cites work: Opérateurs pseudo-différentiels analytiques et problèmes aux limites elliptiques
full work available at URL: https://doi.org/10.1007/bf00971490
OpenAlex ID: W2085964729
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description: scientific article; zbMATH DE number 4153107