| Title | Properties of the Pushforward Map on Test Functions, Measures and Distributions |
| Authors | Niels Christian Overgaard |
| Publication | Doctoral Theses in Mathematical Sciences |
| Year | 2002 |
| Volume | 2001:7 |
| Pages | 115 |
| Document type | Thesis |
| Language | eng |
| Publisher | Niels Chr. Overgaard, Centre of Mathematical Sciences, Dept. of Mathematics, |
| Abstract 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.<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. |
| 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, |
| ISBN/ISSN/Other | ISSN: 1404-0034 ISBN: 91-628-5013-X ISRN: LUTFMA-1013-2001 |
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