The Hilbert transform on the two-sphere: A spectral characterization

DOI10.1007/S11004-010-9278-5zbMath1201.44005OpenAlexW2163220152MaRDI QIDQ600859

Lennart Wietzke, Oliver Fleischmann, Gerald Sommer

Publication date: 3 November 2010

Published in: Mathematical Geosciences (Search for Journal in Brave)

Full work available at URL: https://macau.uni-kiel.de/servlets/MCRFileNodeServlet/macau_derivate_00003000/tr-0924-bericht.pdf

zbMATH Keywords

series expansionHilbert transformCauchy transformspherical harmonicsLaplace equationsignal processingClifford analysisRiesz transformspectral characterizationplane wave decompositionPoisson scale spaceWigner-D functions

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Spherical harmonics (33C55)

Related Items (1)

Convolutions on the sphere: commutation with differential operators

Cites Work

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• On some properties of the Hilbert transform in Euclidean space
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• On the multiscale solution of satellite problems by use of locally supported kernel functions correspondind to equidistributed data on spherical orbits
• The monogenic signal
• On the interplay between the Hilbert transform and conjugate harmonic functions
• Computational Science – ICCS 2005

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