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March 21, 2026Journal of International Crisis and Risk Communication ResearchOpen Access

Wavelet Transform Of Periodic Generalized-Functions

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Implication

Defines wavelet transforms for periodic functions, extending to generalized functions, suggesting new applications for analysis.

Key Points

  • The aim is to define and extend the wavelet transform to larger spaces of generalized functions beyond periodic Schwartz distributions.
  • Defined the wavelet transform for periodic functions.
  • Extended the definition to Beurling ultradistributions and hyperfunctions.
  • Analyzed the growth rate of derivatives of the wavelet transform in relation to the analyzing wavelet.
  • Wavelet transforms of generalized functions yield smooth functions on an infinite cylinder.
  • The growth rate of the derivatives of the wavelet transform is nearly as good as that of the analyzing wavelet.

Cite This Study

A 1995 study studied this question.

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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Hankel, fractional Hankel, and Bessel wavelet transforms of almost periodic signals: product-type and spherical extensions in n variables2026
  2. 2Approximation of Periodic Functions by Wavelet Fourier Series2024 · 1 citations
  3. 3Band-limited wavelets beyond Gevrey regularity2024 · 1 citations
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  5. 5On some $q$-Bessel type continuous wavelet transform2024