New constructions of piecewise-constant wavelets.
New quadrature rules for Bernstein measures on the interval .
New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform.
Non-Lebesgue multiresolution analyses
Classical notions of wavelets and multiresolution analyses deal with the Hilbert space L²(ℝ) and the standard translation and dilation operators. Key in the study of these subjects is the low-pass filter, which is a periodic function h ∈ L²([0,1)) that satisfies the classical quadrature mirror filter equation |h(x)|²+|h(x+1/2)|² = 2. This equation is satisfied almost everywhere with respect to Lebesgue measure on the torus. Generalized multiresolution analyses and wavelets exist in abstract Hilbert...
Non-MSF Wavelets for the Hardy Space H²(ℝ)
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.
Nonnegative linearization for orthogonal polynomials with eventually constant Jacobi parameters
We study the nonnegative product linearization property for polynomials with eventually constant Jacobi parameters. For some special cases a necessary and sufficient condition for this property is provided.
Nonnegative linearization of orthogonal polynomials
Nonperiodic Sampling of Bandlimited Functions on Unions of Rectangular Lattices.
Non-separable bidimensional wavelet bases.
We build orthonormal and biorthogonal wavelet bases of L2(R2) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a two-scale difference equation associated to a FIR filter. Our wavelets are generated from a single compactly supported mother function. However, the regularity of these functions cannot be derived by the same approach as in the one dimensional case. We review existing techniques to evaluate the regularity of...
Non-similarity of Walsh and trigonometric systems
We show that in for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.
Non-standard orthogonality for Meixner polynomials.
Nörlund Summability of Jacobi and Laguerre series.
Norm convergence of Fejér means of two-dimensional Walsh-Fourier series
The main aim of this paper is to prove that there exists a martingale such that the Fejér means of the two-dimensional Walsh-Fourier series of f is not uniformly bounded in the space weak-.
Note on decreasing rearrangement of Fourier series.
Note on some characteristic properties of functions of the second kind
Notes on a family of Riordan arrays and associated integer Hankel transforms.
Numerical experiments in Fourier asymptotics of Cantor measures and wavelets.
O aproximací obrazu v Hilbertově transformací ortogonálními řadami racionálních lomených funkcí
Old Friends Revisited; the Multifunctional Nature of Some Classical Functions.
On 2-orthogonal polynomials of Laguerre type.