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

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

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

Publikations- och innehållstyp

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