Covariant Transform

Preprint English OPEN
Kisil, Vladimir V.;
(2010)
  • Related identifiers: doi: 10.1088/1742-6596/284/1/012038
  • Subject: 43A85, 32M99, 43A32, 46E10, 47A60, 47A67, 47C99, 81R30 | Mathematics - Functional Analysis | Mathematics - Complex Variables | Mathematics - Representation Theory
    arxiv: Mathematics::Functional Analysis

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not... View more
  • References (23)
    23 references, page 1 of 3

    [1] Syed Twareque Ali, Jean-Pierre Antoine, and Jean-Pierre Gazeau, Coherent states, wavelets and their generalizations, Graduate Texts in Contemporary Physics, Springer-Verlag, New York, 2000. MR2002m:81092 ↑1, 2, 3, 4, 8

    [2] Ola Bratteli and Palle E. T. Jorgensen, Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N , Integral Equations Operator Theory 28 (1997), no. 4, 382-443. E-print: arXiv:funct-an/9612003. ↑4

    [3] Jens Gerlach Christensen and Gestur O´ lafsson, Examples of coorbit spaces for dual pairs, Acta Appl. Math. 107 (2009), no. 1-3, 25-48. MR2520008 ↑1, 2

    [4] Jan Cnops and Vladimir V. Kisil, Monogenic functions and representations of nilpotent Lie groups in quantum mechanics, Math. Methods Appl. Sci. 22 (1999), no. 4, 353-373. E-print: arXiv:math/9806150. Zbl 1005.22003. MR1671449 (2000b:81044) ↑4

    [5] M. Duflo and Calvin C. Moore, On the regular representation of a nonunimodular locally compact group, J. Functional Analysis 21 (1976), no. 2, 209-243. MR52#14145 ↑3, 8

    [6] Feichtinger, Hans G. and Groechenig, K.H., Banach spaces related to integrable group representations and their atomic decompositions, I, J. Funct. Anal. 86 (1989), no. 2, 307-340. Zbl 691.46011. ↑1, 2

    [7] Hartmut Fu¨hr, Abstract harmonic analysis of continuous wavelet transforms, Lecture Notes in Mathematics, vol. 1863, Springer-Verlag, Berlin, 2005. MR2130226 (2006m:43003) ↑1, 2

    [8] Loukas Grafakos, Classical Fourier analysis, Second, Graduate Texts in Mathematics, vol. 249, Springer, New York, 2008. MR2445437 ↑4

    [9] Ondrej Hutn´ık, On Toeplitz-type operators related to wavelets, Integral Equations Operator Theory 63 (2009), no. 1, 29-46. MR2480637 ↑3

    [10] Andreas Johansson, Shift-invariant signal norms for fault detection and control, Systems Control Lett. 57 (2008), no. 2, 105-111. MR2378755 (2009d:93035) ↑4

  • Metrics
Share - Bookmark