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Sheaves of Schwartz distributions

Technical Report:

Abstract

The theory of sheaves is a relevant mathematical language for describing the localization principle, known to be valid for the Schwartz distributions (generalized functions). After introducing some fundamentals of sheaves and the basic facts about distribution spaces, the distribution sheaf D{sub {Omega}} of topological C-vector spaces over an open set {Omega} in R{sup n} is systematically studied. A sheaf D{sub M} of distributions on a C{sup {infinity}}-manifold M is then introduced, following a definition of Hoermander`s for its particular elements. Further, a general definition of sheaves on a manifold, that are locally isomorphic to (or, modelled on) a sheaf on R{sup n}, in proposed. The sheaf properties of D{sub M} are studied and this sheaf is shown to be locally isomorphic to D{sub {Omega}}, as a sheaf of topological vector spaces. (author). 14 refs.
Authors:
Publication Date:
Sep 01, 1991
Product Type:
Technical Report
Report Number:
IC-91/272
Reference Number:
SCA: 661100; PA: AIX-23:015325; SN: 92000647054
Resource Relation:
Other Information: PBD: Sep 1991
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL MANIFOLDS; DISTRIBUTION; ALGEBRA; FUNCTIONS; MATHEMATICAL SPACE; TOPOLOGY; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10113305
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE92615217; TRN: XA9130265015325
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
29 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Damyanov, B P. Sheaves of Schwartz distributions. IAEA: N. p., 1991. Web.
Damyanov, B P. Sheaves of Schwartz distributions. IAEA.
Damyanov, B P. 1991. "Sheaves of Schwartz distributions." IAEA.
@misc{etde_10113305,
title = {Sheaves of Schwartz distributions}
author = {Damyanov, B P}
abstractNote = {The theory of sheaves is a relevant mathematical language for describing the localization principle, known to be valid for the Schwartz distributions (generalized functions). After introducing some fundamentals of sheaves and the basic facts about distribution spaces, the distribution sheaf D{sub {Omega}} of topological C-vector spaces over an open set {Omega} in R{sup n} is systematically studied. A sheaf D{sub M} of distributions on a C{sup {infinity}}-manifold M is then introduced, following a definition of Hoermander`s for its particular elements. Further, a general definition of sheaves on a manifold, that are locally isomorphic to (or, modelled on) a sheaf on R{sup n}, in proposed. The sheaf properties of D{sub M} are studied and this sheaf is shown to be locally isomorphic to D{sub {Omega}}, as a sheaf of topological vector spaces. (author). 14 refs.}
place = {IAEA}
year = {1991}
month = {Sep}
}