Wavelet Basis Packets and Wavelet Frame Packets.
Ruilin Long, Wen Chen (1997)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Ruilin Long, Wen Chen (1997)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Cattani, Carlo, Sánchez Ruiz, Luis M. (2004)
International Journal of Mathematics and Mathematical Sciences
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Sheikh, N.A., Mursaleen, M. (2004)
International Journal of Mathematics and Mathematical Sciences
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Marcin Bownik, Gustavo Garrigós (2004)
Studia Mathematica
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We give a characterization of biorthogonal wavelets arising from MRA's of multiplicity D entirely in terms of the dimension function. This improves the previous characterization in [8] removing an unnecessary angle condition. Besides we characterize Riesz wavelets arising from MRA's, and present new proofs based on shift-invariant space theory, generalizing the 1-dimensional results appearing in [17].
Aparna Vyas (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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Considering symmetric wavelet sets consisting of four intervals, a class of non-MSF non-MRA wavelets for L²(ℝ) and dilation 2 is obtained. In addition, we obtain a family of non-MSF non-MRA H²-wavelets which includes the one given by Behera [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178].
Silvia Bertoluzza (2005)
Bollettino dell'Unione Matematica Italiana
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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.
Ü. Lepik, H. Hein (2015)
Waves, Wavelets and Fractals
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In recent times the wavelet methods have obtained a great popularity for solving differential and integral equations. From different wavelet families we consider here the Haar wavelets. Since the Haar wavelets are mathematically most simple to be compared with other wavelets, then interest to them is rapidly increasing and there is a great number of papers,where thesewavelets are used tor solving problems of calculus. An overview of such works can be found in the survey paper by Hariharan...
Matthias Holschneider (1994)
Recherche Coopérative sur Programme n°25
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Roşca, Daniela, Antoine, Jean-Pierre (2009)
Mathematical Problems in Engineering
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Arambašić Ljiljana, Damir Bakić, Rajna Rajić (2010)
Studia Mathematica
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The paper is a continuation of our study of dimension functions of orthonormal wavelets on the real line with dyadic dilations. The main result of Section 2 is Theorem 2.8 which provides an explicit reconstruction of the underlying generalized multiresolution analysis for any MSF wavelet. In Section 3 we reobtain a result of Bownik, Rzeszotnik and Speegle which states that for each dimension function D there exists an MSF wavelet whose dimension function coincides with D. Our method...
Schmeelk, John, Takači, Arpad (1997)
International Journal of Mathematics and Mathematical Sciences
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Biswaranjan Behera (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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All wavelets constructed so far for the Hardy space H²(ℝ) are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.
Hans Triebel (2004)
Banach Center Publications
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Cattani, Carlo (2010)
Mathematical Problems in Engineering
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