An extension of distributional wavelet transform

Volume 115 / 2009

R. Roopkumar Colloquium Mathematicum 115 (2009), 195-206 MSC: 44A15, 46F12. DOI: 10.4064/cm115-2-5


We construct a new Boehmian space containing the space $\tilde{{\scr S}}^\prime (\mathbb{R}^n\times\mathbb{R}_+)$ and define the extended wavelet transform $\mathscr{W}$ of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to $\delta$-convergence as well as $\Delta$-convergence.


  • R. RoopkumarDepartment of Mathematics
    Alagappa University
    Karaikudi 630 003, India

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