## 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.

## 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}

}

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}

}