Hilbert transforms on the sphere with the Clifford algebra setting

DOI10.1007/s00041-009-9062-4zbMath1182.30092OpenAlexW2053967059MaRDI QIDQ2655132

Tao Qian, Yan Yang

Publication date: 22 January 2010

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-009-9062-4

zbMATH Keywords

Poisson kernelClifford analysisCauchy singular integralHilbert transformationSchwarz kernel

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35)

Related Items (14)

A class of iterative greedy algorithms related to Blaschke product ⋮ Positive-instantaneous frequency and approximation ⋮ Phase derivative of monogenic signals in higher dimensional spaces ⋮ Schwarz problems for poly-Hardy space on the unit ball ⋮ Uncertainty principle and phase-amplitude analysis of signals on the unit sphere ⋮ Orthogonalization in Clifford Hilbert modules and applications ⋮ Hardy Spaces for the Three-Dimensional Vekua Equation ⋮ A Theory on Non-Constant Frequency Decompositions and Applications ⋮ Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis ⋮ Riemann-Hilbert problems for poly-Hardy space on the unit ball ⋮ Hilbert transform for the three-dimensional Vekua equation ⋮ A new quaternion hyper-complex space with hyper argument and basic functions via quaternion dynamic equations ⋮ Adaptive Fourier decomposition of functions in quaternionic Hardy spaces ⋮ Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem

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