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

Summary, in English

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.

• Author: Niels Christian Overgaard
• Department/s: Mathematics (Faculty of Engineering); Partial differential equations
• Publishing year: 2002
• Language: English
• Publication/Series: Doctoral Theses in Mathematical Sciences
• Volume: 2001:7
• Document type: Dissertation
• Publisher: Niels Chr. Overgaard, Centre of Mathematical Sciences, Dept. of Mathematics,
• Topic: Mathematics
• 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
• Status: Published
• Research group: Partial differential equations
• Supervisor: [unknown] [unknown]
• ISBN/ISSN/Other: ISSN: 1404-0034; ISBN: 91-628-5013-X; ISRN: LUTFMA-1013-2001
• Defence date: 26 April 2002
• Defence time: 13:15
• Defence place: MH:C
• Opponent: Jan-Erik Björk