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Frame Expansions of Test Functions, Tempered Distributions, and Ultradistributions

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Analysis, Probability, Applications, and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

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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.

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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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Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia

    Stevan Pilipović

  2. Acoustics Research Institute, Austrian Academy of Sciences, Vienna, Austria

    Diana T. Stoeva

Authors
  1. Stevan Pilipović
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  2. Diana T. Stoeva
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Corresponding author

Correspondence to Diana T. Stoeva .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Karl‐Olof Lindahl

  2. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Torsten Lindström

  3. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

  5. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Patrik Wahlberg

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Pilipović, S., Stoeva, D.T. (2019). Frame Expansions of Test Functions, Tempered Distributions, and Ultradistributions. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_44

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