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On the adaptive wavelet estimation of a multidimensional regression function under α -mixing dependence: Beyond the standard assumptions on the noise

Christophe Chesneau (2013)

Commentationes Mathematicae Universitatis Carolinae

We investigate the estimation of a multidimensional regression function f from n observations of an α -mixing process ( Y , X ) , where Y = f ( X ) + ξ , X represents the design and ξ the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of f in its construction) or it is supposed that ξ is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....

On the boundary convergence of solutions to the Hermite-Schrödinger equation

Peter Sjögren, J. L. Torrea (2010)

Colloquium Mathematicae

In the half-space ℝ d × ℝ ₊ , consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on ℝ d . We prove a formula that links the solution of this problem to that of the classical Schrödinger equation. It shows that mixed norm estimates for the Hermite-Schrödinger equation can be obtained immediately from those known in the classical case. In one space dimension, we deduce sharp pointwise convergence results at the boundary by means of this link.

On the bundle convergence of double orthogonal series in noncommutative L 2 -spaces

Ferenc Móricz, Barthélemy Le Gac (2000)

Studia Mathematica

The notion of bundle convergence in von Neumann algebras and their L 2 -spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men’shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series....

On the computation of scaling coefficients of Daubechies' wavelets

Dana Černá, Václav Finěk (2004)

Open Mathematics

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.

On the conjecture of Gát.

Goginava, Ushangi (2004)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On the exact values of coefficients of coiflets

Dana Černá, Václav Finěk, Karel Najzar (2008)

Open Mathematics

In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling coefficients...

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