Properties of the Pushforward Map on Test Functions, Measures and Distributions
(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 welldefined, 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 welldefined, 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:
https://lup.lub.lu.se/record/20535
 author
 Overgaard, Niels Christian ^{LU}
 supervisor
 opponent

 Björk, JanErik, Mathematics, Stockholm University
 organization
 publishing date
 2002
 type
 Thesis
 publication status
 published
 subject
 keywords
 Matematik, Mathematics, wavefront sets., oscillatory integrals, BernsteinSato 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
 20020426 13:15:00
 external identifiers

 other:ISRN: LUTFMA10132001
 ISSN
 14040034
 ISBN
 916285013X
 language
 English
 LU publication?
 yes
 id
 5b1ad03d2f294e2d81ea60a94dd708df (old id 20535)
 date added to LUP
 20160401 16:30:36
 date last changed
 20190521 13:29:19
@phdthesis{5b1ad03d2f294e2d81ea60a94dd708df, 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 welldefined, 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 = {916285013X}, issn = {14040034}, language = {eng}, 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}, }