Graded differential equations and Dirac type operators
type: Item
instance of: scholarly article
title: Graded differential equations and Dirac type operators
zbMATH Open document ID: 0931.35005
DOI: 10.1023/A:1006177901138
author: Lev V. Zilbergleit
published in: Acta Applicandae Mathematicae
publication date: 2000-02-20T00:00:00Z
review text: Fundamental ideas of geometric asymptotics of linear differential operators are described in terms of graded category within the framework of the jet theory of sections of vector bundles. In more detail, the author recalls the category of graded and filtered vector spaces and algebras, linear differential operators on vector bundles including prolongations and symbols, the filtrations associated with wave-like solutions \((\hbar\)-adic filtrations) and the corresponding characteristic submanifolds and transfer operators. Then the results are applied to the Dirac operator where the transfer describing the propagation of singularities yields an invariant definition of the Pauli operator.
reviewed by: Jan Chrastina
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58J45
Mathematics Subject Classification ID: 35A21
Mathematics Subject Classification ID: 58K35
zbMATH DE Number: 1340266
zbMATH Keywords: jet theory of sections of vector bundles
zbMATH Keywords: filtrations associated with wave-like solutions
MaRDI profile type: Publication
full work available at URL: a:1006177901138
OpenAlex ID: W94692371
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description: scientific article; zbMATH DE number 1340266