On the uniform convergence and -convergence of double Fourier series with respect to the Walsh-Kaczmarz system.
On the uniform convergence and L¹-convergence of double Walsh-Fourier series
In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in -norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by we mean , the collection of uniformly W-continuous functions f(x, y), endowed with the...
On the weighted estimate of the Bergman projection
We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.
On three problems from the Scottish Book connected with orthogonal systems
On unconditional convergence of Haar series
On Wavelet Sets.
On weighted transplantation and multipliers for Laguerre expansions.
On Y. Nievergelt's Inversion Formula for the Radon Transform
Mathematics Subject Classification 2010: 42C40, 44A12.In 1986 Y. Nievergelt suggested a simple formula which allows to reconstruct a continuous compactly supported function on the 2-plane from its Radon transform. This formula falls into the scope of the classical convolution-backprojection method. We show that elementary tools of fractional calculus can be used to obtain more general inversion formulas for the k-plane Radon transform of continuous and L^p functions on R^n for all 1 ≤ k < n....
On zeros of reciprocal polynomials of odd degree.
On zeros of regular orthogonal polynomials on the unit circle
A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.
Once more on the double Fourier-Haar series
Ondelettes, analyses multirésolutions et filtres miroirs en quadrature
Ondelettes, espaces d’interpolation et applications
Nous établissons des résultats d’interpolation non-standards entre les espaces de Besov et les espaces et , avec des applications aux lemmes de régularité en moyenne et aux inégalités de type Gagliardo-Nirenberg. La preuve de ces résultats utilise les décompositions dans des bases d’ondelettes.
Ondelettes et bases hilbertiennes.
Ondelettes et espaces de Besov.
Ondelettes et poids de Muckenhoupt
We study, for a basis of Hölderian compactly supported wavelets, the boundedness and convergence of the associated projectors on the space for some p in ]1,∞[ and some nonnegative Borel measure μ on ℝ. We show that the convergence properties are related to the criterion of Muckenhoupt.
Ondelettes generalisées et fonctions d'échelle à support compact.
We show that to any multi-resolution analysis of L2(R) with multiplicity d, dilation factor A (where A is an integer ≥ 2) and with compactly supported scaling functions we may associate compactly supported wavelets. Conversely, if (Ψε,j,k = Aj/2 Ψε (Ajx - k)), 1 ≤ ε ≤ E and j, k ∈ Z, is a Hilbertian basis of L2(R) with continuous compactly supported mother functions Ψε, then it is provided by a multi-resolution analysis with dilation factor A, multiplicity d = E / (A - 1) and with compactly supported...
Ondelettes sur l'intervalle.
Open problems in constructive function theory.
Operators preserving orthogonality of polynomials
Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions for polynomials...