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Multi-dimensional Summability Theory and Continuous Wavelet Transform

In: Current Topics in Summability Theory and Applications

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  • Ferenc Weisz

    (Eötvös L. University, Department of Numerical Analysis)

Abstract

The connection between multi-dimensional summability theory and continuous wavelet transform is investigated. Two types of $$\theta $$ θ -summability of Fourier transforms are considered, the circular and rectangular summability. Norm and almost everywhere convergence of the $$\theta $$ θ -means are shown for both types. The inversion formula for the continuous wavelet transform is usually considered in the weak sense. Here, the inverse wavelet transform is traced back to summability means of Fourier transforms. Using the results concerning the summability of Fourier transforms, norm and almost everywhere convergence of the inversion formula are obtained for functions from the $$L_p$$ L p and Wiener amalgam spaces.

Suggested Citation

  • Ferenc Weisz, 2016. "Multi-dimensional Summability Theory and Continuous Wavelet Transform," Springer Books, in: Hemen Dutta & Billy E. Rhoades (ed.), Current Topics in Summability Theory and Applications, pages 241-311, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-0913-6_6
    DOI: 10.1007/978-981-10-0913-6_6
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