Continuous wavelet transform of Schwartz distributions

DOI10.1216/RMJ-2019-49-6-2005zbMath1428.42074MaRDI QIDQ2008595

Yanyan Li

Publication date: 26 November 2019

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1572746431

zbMATH Keywords

window functionswavelet transformSchwartz distributionscontinuous wavelet transformintegral transform of generalized functions

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Integral transforms in distribution spaces (46F12) Operations with distributions and generalized functions (46F10) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (4)

Continuous wavelet transform of Schwartz distributions in \(\mathcal{D}'(\mathbb{R}^{n}),n\geq 1\) ⋮ The Bessel wavelet transform of distributions in βμ′-space ⋮ The Bessel wavelet transform of distributions in DL2′-type space ⋮ Wavelet transform of multiplicators and convolutors for ultradistributions

Cites Work

• Inverse continuous wavelet transform in pringsheim's sense on Wiener amalgam spaces
• Nonhomogeneous wavelet systems in high dimensions
• Pairs of frequency-based nonhomogeneous dual wavelet frames in the distribution space
• The wavelet transform
• Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition
• Convergence of the inverse continuous wavelet transform in Wiener amalgam spaces
• Continuous wavelet transform of Schwartz tempered distributions in \(S^\prime (\mathbb{R}^n)\)
• Inversion formulas for the continuous wavelet transform
• Analytic functions and the Fourier transform of distributions. I, II
• The continuous wavelet transform in n-dimensions
• The continuous wavelet transform and window functions
• Ten Lectures on Wavelets
• Singularities of Distributions Via the Wavelet Transform
• Continuous wavelet transform of Schwartz tempered distributions
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