N-dimensional affine Weyl-Heisenberg wavelets
C. Kalisa, B. Torrésani (1993)
Annales de l'I.H.P. Physique théorique
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C. Kalisa, B. Torrésani (1993)
Annales de l'I.H.P. Physique théorique
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Takeshi Kawazoe (1996)
Annales de l'I.H.P. Physique théorique
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Wilczok, Elke (2000)
Documenta Mathematica
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B. Torresani (1992)
Annales de l'I.H.P. Physique théorique
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Mei, Shu-Li, Lv, Hong-Liang, Ma, Qin (2008)
Mathematical Problems in Engineering
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K. Trimèche (1996)
Collectanea Mathematica
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In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
C. Bonatti, H. Hattab, E. Salhi (2011)
Fundamenta Mathematicae
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Let G ⊂ Homeo(E) be a group of homeomorphisms of a topological space E. The class of an orbit O of G is the union of all orbits having the same closure as O. Let E/G̃ be the space of classes of orbits, called the quasi-orbit space. We show that every second countable T₀-space Y is a quasi-orbit space E/G̃, where E is a second countable metric space. The regular part X₀ of a T₀-space X is the union of open subsets homeomorphic to ℝ or to 𝕊¹. We give a characterization of the spaces X...
Cornelia Kaiser, Lutz Weis (2008)
Studia Mathematica
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We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.
Schmeelk, John, Takači, Arpad (1997)
International Journal of Mathematics and Mathematical Sciences
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Jouini, Abdellatif (2004)
International Journal of Mathematics and Mathematical Sciences
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Stéphane Jaffard (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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Let be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with , and denoted by . We show how properties of are transferred into properties of . Applications are given in multifractal analysis.