Malotalasna transformacija u prostorima distribucija i ultradistribucija i teoreme Abelovog i Tauberovog tipa

Rakić, Dušan

Wavelet Transform of Distributions and Ultradistributions and Abelian and Tauberian Theorems

Abstract

U disertaciji se navode definicije i svojstva malotalasne transformacije i kvaziasimptotskog ponaˇsanja distribucija. Teoreme Abelovog i Tauberovog tipa su koriˇs´cene za asimptotsku analizu temperiranih distribucija, u odnosu na njihovu malotalasnu transformaciju. Takode, prouˇcavana je i malotalasna transformacija ultradiferencijabilnih funkcija i temperiranih ultradistribucija.

In thesis we give basic notions of wavelet transform and quasiasymptotic behavior of distributions. Via Abelian and Tauberian type of theorems we study quasiasymptotic behavior of tempered distributions, related to their wavelet transform. Further, we study wavelet transform of ultradifferential functions and tempered ultradistributions.

Faculty:
University of Novi Sad, Faculty of Science
Date:
18-12-2010

Keywords:

Prostori distribucija / spaces of distributions / malotalasna transformacija / kvaziasimptotika / prostori temperiranih ultradistribucija / wavelet transform / quasiasymptotics / spaces of tempered ultradistributions

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