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A note on wavelet subspaces

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Abstract

The wavelet subspaces of the space of square integrable functions on the affine group with respect to the left invariant Haar measure dν are studied using the techniques from Vasilevski (Integral Equ. Operator Theory 33:471–488, 1999) with respect to wavelets whose Fourier transforms are related to Laguerre polynomials. The orthogonal projections onto each of these wavelet subspaces are described and explicit forms of reproducing kernels are established. Isomorphisms between wavelet subspaces are given.

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References

  1. Ali S.T., Antoine J.-P., Gazeau J.-P.: Coherent States, Wavelets and Their Generalizations, Graduate Texts in Contemporary Physics. Springer, New York (2000)

    Google Scholar 

  2. Abramowitz M., Stegun I.A.: Handbook of Mathematical Functions. Dover, New York (1970)

    Google Scholar 

  3. Calderón A.: Intermediate spaces and interpolation, the complex method. Studia Math. 24, 113–190 (1964)

    MATH  MathSciNet  Google Scholar 

  4. Grossmann A., Morlet J., Paul T.: Transforms associated to square integrable group representations II: Examples. Ann. Inst. Henri. Poincaré 45, 293–309 (1986)

    MATH  MathSciNet  Google Scholar 

  5. Hutník O.: On the structure of the space of wavelet transforms. C. R. Acad. Sci. Paris Sér I Math. 346, 649–652 (2008)

    MATH  Google Scholar 

  6. Jiang Q., Peng L.: Wavelet transform and Toeplitz–Hankel type operators. Math. Scand. 70, 247–264 (1992)

    MATH  MathSciNet  Google Scholar 

  7. Jiang Q., Peng L.: Toeplitz and Hankel type operators on the upper half-plane. Integral Equ. Operator Theory 15, 744–767 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Paul T.: Functions analytic on the half-plane as quantum mechanical states. J. Math. Phys. 25, 3252–3262 (1984)

    Article  MathSciNet  Google Scholar 

  9. Vasilevski N.L.: On the structure of Bergman and poly-Bergman spaces. Integral Equ. Operator Theory 33, 471–488 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Vasilevski, N.L.: Commutative Algebras of Toeplitz Operators on the Bergman Space, Series: Operator Theory: Advances and Applications, vol. 185. Birkhäuser, Basel (2008)

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  1. Ondrej Hutník

    Present address: , Jesenná 5, 041 54, Kosice, Slovakia

Authors and Affiliations

  1. Faculty of Science, Institute of Mathematics, Pavol Jozef Šafárik University in Košice, Kosice, Slovakia

    Ondrej Hutník

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  1. Ondrej Hutník
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Correspondence to Ondrej Hutník.

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Communicated by K.H. Gröchenig.

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Hutník, O. A note on wavelet subspaces. Monatsh Math 160, 59–72 (2010). https://doi.org/10.1007/s00605-008-0084-9

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  • DOI: https://doi.org/10.1007/s00605-008-0084-9

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