The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields

The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields

Global and local regularity of functions in anisotropic function spaces is analyzed in the common framework provided by hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities derived from the coefficients of hyperbolic wavelet decompositio...

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Veröffentlicht in:Revista matemática iberoamericana 2015-01, Vol.31 (1), p.313-348
Hauptverfasser: Abry, Patrice, Clausel, Marianne, Jaffard, Stéphane, Roux, Stéphane, Vedel, Béatrice
Format: Artikel
Sprache:eng
Schlagworte:
Fourier analysis
Functional analysis
Mathematics
Statistics
Statistics Theory
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Zusammenfassung:Global and local regularity of functions in anisotropic function spaces is analyzed in the common framework provided by hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities derived from the coefficients of hyperbolic wavelet decompositions. A multifractal analysis is introduced, that jointly accounts for scale invariance and anisotropy, and its properties are investigated.
ISSN:0213-2230
2235-0616
DOI:10.4171/RMI/836