Sampling Theory for Functions with Fractal Spectrum

DOI10.1080/10586458.2001.10504681zbMath1014.94006OpenAlexW2015067834MaRDI QIDQ3146579

Robert S. Strichartz, Nina N. Huang

Publication date: 12 September 2002

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1069855261

zbMATH Keywords

numerical experimentsbandlimited functionssampling formulasfractal spectrumasymptotic behavior of sampling functions

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fractals (28A80)

Related Items (11)

Duality questions for operators, spectrum and measures ⋮ Wavelets on fractals ⋮ A property of Pisot numbers and Fourier transforms of self-similar measures ⋮ Spectral properties of a class of Moran measures on \(\mathbb{R}^2\) ⋮ Spectrality of generalized Sierpinski-type self-affine measures ⋮ Convergence of mock Fourier series ⋮ Asymptotic behaviour of multiperiodic functions scaled by Pisot numbers. ⋮ Sampling and interpolation of cumulative distribution functions of Cantor sets in \([0,1\)] ⋮ Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms ⋮ A Paley-Wiener type theorem for singular measures on \((-1/2, 1/2)\) ⋮ On spectral Cantor measures

Uses Software

• MATHLAB

Cites Work

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• Dense analytic subspaces in fractal \(L^2\)-spaces
• Remarks on ``Dense analytic subspaces in fractal \(L^2\)-spaces by P. E. T. Jorgensen and S. Pedersen
• Asymptotic behavior of multiperiodic functions \(G(x)=\prod_{n=1}^\infty g(x/2^n)\)
• Mean dimension of function classes with Lebesgue measurable spectral sets
• The shape of the error in wavelet approximation and piecewise linear interpolation
• Mock Fourier series and transforms associated with certain Cantor measures
• Numerical Experiments in Fourier Asymptotics of Cantor Measures and Wavelets
• Self-Similar Measures and Their Fourier Transforms. II

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