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Frame Expansions of Test Functions, Tempered Distributions, and Ultradistributions

  • Stevan Pilipović
  • Diana T. StoevaEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The paper is devoted to frame expansions in Fréchet spaces. First we review some results which concern series expansions in general Fréchet spaces via Fréchet and General Fréchet frames. Then we present some new results on series expansions of tempered distributions and ultradistributions, and the corresponding test functions, via localized frames and coefficients in appropriate sequence spaces.

Notes

Acknowledgements

The authors acknowledge support from the Multilateral S&T Danube-Cooperation Project TIFMOFUS (“Time-Frequency Methods for Operators and Function Spaces”; MULT_DR 01/2017), the Austrian Science Fund (FWF) START-project FLAME (“Frames and Linear Operators for Acoustical Modeling and Parameter Estimation”; Y 551-N13), and the Project 174024 of the Serbian Ministry of Sciences. The second author is grateful for the hospitality of the University of Novi Sad, where most of the research on the presented topic was done. The authors express their gratitude to the referee for the valuable advices.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of Novi SadNovi SadSerbia
  2. 2.Acoustics Research InstituteAustrian Academy of SciencesViennaAustria

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