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 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:
https://lup.lub.lu.se/record/20535
- author
- Overgaard, Niels Christian LU
- supervisor
- opponent
-
- Björk, Jan-Erik, Mathematics, Stockholm University
- organization
- publishing date
- 2002
- 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 13:15:00
- 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
- 2016-04-01 16:30:36
- date last changed
- 2019-05-21 13:29:19
@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}}, 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}}, 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}}, }