Displaying similar documents to “Contributions to local and microlocal analysis, an overwiew”

Pointwise smoothness, two-microlocalization and wavelet coefficients.

Stéphane Jaffard (1991)

Publicacions Matemàtiques

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In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces C , and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet...

Wavelet frames for distributions; local and pointwise regularity

Hans Triebel (2003)

Studia Mathematica

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This paper deals with wavelet frames for a large class of distributions on euclidean n-space, including all compactly supported distributions. These representations characterize the global, local, and pointwise regularity of the distribution considered.

Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.

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*.

Wavelet transform and binary coalescence detection

Jean-Michel Innocent, Bruno Torrésani (1997)

Banach Center Publications

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We give a short account of some time-frequency methods which are relevant in the context of gravity waves detection. We focus on the case of wavelet analysis which we believe is particularly appropriate. We show how wavelet transforms can lead to efficient algorithms for detection and parameter estimation of binary coalescence signals. In addition, we give in an appendix some of the ingredients needed for the construction of discrete wavelet decompositions and corresponding fast algorithms. ...

An extension of distributional wavelet transform

R. Roopkumar (2009)

Colloquium Mathematicae

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We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 𝓦 of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to δ-convergence as well as Δ-convergence.