Wavelet transforms in generalized Fock spaces.
Schmeelk, John, Takači, Arpad (1997)
International Journal of Mathematics and Mathematical Sciences
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Schmeelk, John, Takači, Arpad (1997)
International Journal of Mathematics and Mathematical Sciences
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Abdolaziz Abdollahi, Jahangir Cheshmavar, Mohsen Taghavi (2011)
Open Mathematics
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In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.
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...
Roşca, Daniela, Antoine, Jean-Pierre (2009)
Mathematical Problems in Engineering
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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.
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.
Cattani, Carlo, Sánchez Ruiz, Luis M. (2004)
International Journal of Mathematics and Mathematical Sciences
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Dana Černá, Václav Finěk (2004)
Open Mathematics
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In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.
Cattani, Carlo (2010)
Mathematical Problems in Engineering
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Jouini, Abdellatif (2004)
International Journal of Mathematics and Mathematical Sciences
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