Note on a Conjecture of Sierksma.
A. Vucic, R.T. Zivaljevic (1993)
Discrete & computational geometry
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A. Vucic, R.T. Zivaljevic (1993)
Discrete & computational geometry
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D.Q. Naiman, H.P. Wynn (1993)
Discrete & computational geometry
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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].
N. L. White (1989)
Discrete & computational geometry
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Krichevskii, Rafail, Potapov, Vladimir (1996)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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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...
Strömberg, Jan-Olov (1998)
Documenta Mathematica
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W. Narkiewicz (1977)
Colloquium Mathematicae
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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...
Cattani, Carlo, Ciancio, Armando (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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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.
K. Kubota (1977)
Acta Arithmetica
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Barbara Wolnik (2006)
Banach Center Publications
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We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.
András Biró (2003)
Acta Arithmetica
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G. Besson (2009)
Bollettino dell'Unione Matematica Italiana
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Cattani, Carlo, Sánchez Ruiz, Luis M. (2004)
International Journal of Mathematics and Mathematical Sciences
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