Advertisement

Riesz Bases Multipliers

  • Diana T. StoevaEmail author
  • Peter Balazs
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 236)

Abstract

The paper concerns frame multipliers when one of the involved sequences is a Riesz basis. We determine the cases when the multiplier is well defined and invertible, well defined and not invertible, respectively not well defined.

Keywords

Riesz bases frame multipliers 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Balazs, Basic definition and properties of Bessel multipliers. J. Math. Anal. Appl. 325(1) (2007), 571–585,MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    P. Balazs, J.-P. Antoine, A. Grybos, Weighted and controlled frames: Mutual relationship and first numerical properties. Int. J. Wavelets Multiresolut. Inf. Process. 8(1) (2010), 109–132.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    P. Balazs, B. Laback, G .Eckel,W.A. Deutsch, Time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking. IEEE Trans. Speech Audio Process. 18(1) (2010), 34–49.CrossRefGoogle Scholar
  4. 4.
    P. Balazs, D. T. Stoeva, J.-P. Antoine, Classification of General Sequences Frame- Related Operators. Sampl. Theory Signal Image Process. 10(1-2) (2011), 151–170.MathSciNetzbMATHGoogle Scholar
  5. 5.
    J. Benedetto, G . Pfander, Frame expansions for Gabor multipliers. Appl. Comput. Harmon. Anal. 20(1) (2006), 26–40.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    O. Christensen, An Introduction to Frames and RieszBases . Birkhäuser, 2003.Google Scholar
  7. 7.
    P. Depalle, R. Kronland-Martinet, B. Torrésani, Time-frequency multipliers for sound synthesis. In: Proceedings of the Wavelet XII conference, SPIE annual Symposium, San Diego, 2007.Google Scholar
  8. 8.
    H.G . Feichtinger, K. Nowak, A first survey of Gabor multipliers. Birkhäuser, Boston, 2003, Ch. 5, pp. 99–128.Google Scholar
  9. 9.
    H.G. Feichtinger, G. Narimani, Fourier multipliers of classical modulation spaces, Appl. Comput. Harmon. Anal. 21(3) (2006) 349–359.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    C. Heil, A Basis Theory Primer. Birkhäuser, Boston, 2011.Google Scholar
  11. 11.
    G. Matz and F. Hlawatsch, Linear Time-Frequency Filters: On-line Algorithms and Applications. Eds. A. Papandreou-Suppappola, Boca Raton (FL): CRC Press, 2002, Ch. 6 in “Application in Time-Frequency Signal Processing”, pp. 205–271.Google Scholar
  12. 12.
    D.T. Stoeva and P. Balazs. Weighted frames and frame multipliers. Annual of the University of Architecture, Civil Engineering and Geodesy, Vol. XLIII-XLIV 2004- 2009 (Fasc. II) (2012), pp. 33–42.Google Scholar
  13. 13.
    D.T. Stoeva and P. Balazs. Invertibility of Multipliers. Appl. Comput. Harmon. Anal. 33(2) (2012), 292–299.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    D.T. Stoeva and P. Balazs, Canonical forms of unconditionally convergent multipliers. J. Math. Anal. Appl. 399(1) (2013), 252–259.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    D.T. Stoeva and P. Balazs, Detailed characterization of unconditional convergence and invertibility of multipliers. Sampl. Theory Signal Image Process. 12(2) (2013), to appear.Google Scholar
  16. 16.
    D.T. Stoeva and P. Balazs, Representation of the inverse of a multiplier as a multiplier. arXiv:1108.6286, 2011.Google Scholar
  17. 17.
    R.M. Young, An Introduction to Nonharmonic Fourier Series. Academic Press, New York and London, 1980.Google Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Acoustics Research InstituteViennaAustria

Personalised recommendations