An affirmative result of the open question on determining function jumps by spline wavelets

DOI10.1007/s10114-017-6321-1zbMath1425.42006OpenAlexW2769593272MaRDI QIDQ1637080

Haiying Zhang, Xian Liang Shi, Jian-zhong Wang

Publication date: 7 June 2018

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-017-6321-1

zbMATH Keywords

jumpB-spline wavelets

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Conjugate functions, conjugate series, singular integrals (42A50)

Cites Work

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• Determination of jumps for functions based on Malvar-Coifman-Meyer conjugate wavelets
• Detection of edges in spectral data
• On \(L^ p\)-boundedness of affine frame operators
• Local convergence for wavelet expansions
• Determination of the jumps of a bounded function by its Fourier series
• Determination of jumps in terms of Abel-Poisson means
• Determination of jumps in terms of derivative convolution operators
• Applications of conjugate operators to determination of jumps for functions
• Concentration factors for functions with harmonic bounded mean variation
• Determination of jumps in terms of spectral data
• Determination of jumps via advanced concentration factors
• Determination of the jump of a function of bounded \(p\)-variation by its Fourier series
• On Compactly Supported Spline Wavelets and a Duality Principle
• Ferenc Lukács type theorems in terms of the Abel-Poisson mean of conjugate series

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