Using methods from [9] we prove the almost everywhere convergence of the Cesàro means of Laguerre series associated with the system of Laguerre functions , n = 0,1,2,..., a ≥ 0. The novel ingredient we add to our previous technique is the weights theory. We also take the opportunity to comment and slightly improve on our results from [9].
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
We study sufficient conditions on the weight w, in terms of membership in the classes, for the spline wavelet systems to be unconditional bases of the weighted space . The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.
We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear invertible map A: ℝⁿ → ℝⁿ such that A(ℤⁿ) ⊂ ℤⁿ and all (complex) eigenvalues of A have modulus greater than 1. This characterization involves the notion of filter multiplier of such a multiresolution analysis. Moreover, the paper contains a characterization of the measurable functions which...
Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a...
We prove the Schatten-Lorentz ideal criteria for commutators of multiplications and projections based on the Calderón reproducing formula and the decomposition theorem for the space of symbols corresponding to commutators in the Schatten ideal.
A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with...
In this paper, we present the simple and double compression algorithms with an error control for compressing satellite data corresponding to several revolutions. The compressions are performed by means of approximations in the norm L∞ by finite series of Chebyshev polynomials, with their known properties of fast evaluation, uniform distribution of the error, and validity over large intervals of time. By using the error control here introduced, the number of terms of the series is given automatically...