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Properties of the Pushforward Map on Test Functions, Measures and Distributions

Overgaard, Niels Christian LU (2002) In Doctoral Theses in Mathematical Sciences 2001:7.
Abstract
The subject of this thesis is the pushforward map on compactly supported distributions induced by a smooth mapping. Being the adjoint of the natural pullback operation on the class of smooth functions, the pushforward map is always well-defined, and as such it must be regarded as one of the fundamental operations of distribution theory.



This thesis has two main aims: The first of these is to give a clear exposition of the properties of the pushforward map associated with a smooth map between open subsets of Euclidean space. The second aim is to investigate the connection between the pushforward by a function f and the asymptotic behavior at infinity of oscillatory integrals with f as phase function. Particular attention... (More)
The subject of this thesis is the pushforward map on compactly supported distributions induced by a smooth mapping. Being the adjoint of the natural pullback operation on the class of smooth functions, the pushforward map is always well-defined, and as such it must be regarded as one of the fundamental operations of distribution theory.



This thesis has two main aims: The first of these is to give a clear exposition of the properties of the pushforward map associated with a smooth map between open subsets of Euclidean space. The second aim is to investigate the connection between the pushforward by a function f and the asymptotic behavior at infinity of oscillatory integrals with f as phase function. Particular attention will be paid to Palamodov's conjecture (in the category of smooth functions), to which we give some partial answers. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Björk, Jan-Erik, Mathematics, Stockholm University
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Matematik, Mathematics, wavefront sets., oscillatory integrals, Bernstein-Sato polynomials, Palamodov's conjecture, image directe, Pushforward map, pullback map, Mathematical logic, set theory, combinatories, Matematisk logik, mängdlära, kombinatorik
in
Doctoral Theses in Mathematical Sciences
volume
2001:7
pages
115 pages
publisher
Niels Chr. Overgaard, Centre of Mathematical Sciences, Dept. of Mathematics,
defense location
MH:C
defense date
2002-04-26 13:15
external identifiers
  • other:ISRN: LUTFMA-1013-2001
ISSN
1404-0034
ISBN
91-628-5013-X
language
English
LU publication?
yes
id
5b1ad03d-2f29-4e2d-81ea-60a94dd708df (old id 20535)
date added to LUP
2007-05-28 09:35:19
date last changed
2017-02-13 14:18:27
@phdthesis{5b1ad03d-2f29-4e2d-81ea-60a94dd708df,
  abstract     = {The subject of this thesis is the pushforward map on compactly supported distributions induced by a smooth mapping. Being the adjoint of the natural pullback operation on the class of smooth functions, the pushforward map is always well-defined, and as such it must be regarded as one of the fundamental operations of distribution theory.<br/><br>
<br/><br>
This thesis has two main aims: The first of these is to give a clear exposition of the properties of the pushforward map associated with a smooth map between open subsets of Euclidean space. The second aim is to investigate the connection between the pushforward by a function f and the asymptotic behavior at infinity of oscillatory integrals with f as phase function. Particular attention will be paid to Palamodov's conjecture (in the category of smooth functions), to which we give some partial answers.},
  author       = {Overgaard, Niels Christian},
  isbn         = {91-628-5013-X},
  issn         = {1404-0034},
  keyword      = {Matematik,Mathematics,wavefront sets.,oscillatory integrals,Bernstein-Sato polynomials,Palamodov's conjecture,image directe,Pushforward map,pullback map,Mathematical logic,set theory,combinatories,Matematisk logik,mängdlära,kombinatorik},
  language     = {eng},
  pages        = {115},
  publisher    = {Niels Chr. Overgaard, Centre of Mathematical Sciences, Dept. of Mathematics,},
  school       = {Lund University},
  series       = {Doctoral Theses in Mathematical Sciences},
  title        = {Properties of the Pushforward Map on Test Functions, Measures and Distributions},
  volume       = {2001:7},
  year         = {2002},
}