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