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Stockwell-like frames for Sobolev spaces

  • Ubertino Battisti
  • Michele Berra
  • Anita Tabacco
Article
  • 24 Downloads

Abstract

We construct a family of frames describing the norm and seminorm of the space \(H^s(\mathbb {R}^d)\). We also characterise Besov spaces modeled on \(L^2(\mathbb {R}^d)\). Our work is inspired by the discrete orthonormal Stockwell transform introduced by R.G. Stockwell, which provides a time-frequency localised version of the Fourier basis of \(L^2([0,1])\). This approach is a hybrid between Gabor and Wavelet frames. We construct explicit and computable examples of these frames, discussing their properties and comparing them with the existing literature.

Keywords

Frames Stockwell transform Sobolev spaces Decomposition spaces 

Mathematics Subject Classification

42C15 42C40 46E35 

Notes

Acknowledgements

We thank Fabio Nicola and Sandra Saliani for useful discussions on the subject. We also acknowledge the anonymous referee who helped improving the quality of the paper. We acknowledge that the present research has been partially supported by MIUR grant Dipartimenti di Eccellenza 2018-2022.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Politecnico di TorinoTurinItaly
  2. 2.MIURCavallermaggioreItaly

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