This article is cited in 9 papers

Meyer Wavelets with Least Uncertainty Constant

E. A. Lebedeva^a, V. Yu. Protasov<sup>b

a</sup> Kursk State University
^b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In the present paper, we construct a system of Meyer wavelets with least possible uncertainty constant. The uncertainty constant minimization problem is reduced to a convex variational problem whose solution satisfies a second-order nonlinear differential equation. Solving this equation numerically, we obtain the desired system of wavelets.

Keywords: Meyer wavelet, uncertainty constant, variational problem, second-order nonlinear differential equation, Sobolev space, Fourier transform.

UDC: 517.518.36+517.972.9

Received: 28.08.2007

DOI: 10.4213/mzm4002

 English version: Mathematical Notes, 2008, 84:5, 680–687

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