Affine Systems in L...(...) II: Dual Systems.
Algorithm 79. An algorithm for Fourier series expansion in a subinterval of the circumference
Almost everywhere convergence of Laguerre series
Almost everywhere convergence of Marcinkiewicz means of Fourier series on the group of 2-adic integers
We prove the almost everywhere convergence of the Marcinkiewicz means of integrable functions σₙf → f for every f ∈ L¹(I²), where I is the group of 2-adic integers.
Almost everywhere convergence of some summabillity methods for Laguerre series
Almost everywhere convergence of subsequence of logarithmic means of Walsh-Fourier series.
Almost everywhere convergence of Walsh Fourier series of -functions
Almost everywhere summability of Laguerre series
We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions , n = 0,1,2,..., in , a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function , 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.
Almost everywhere summability of Laguerre series. II
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].
Alternative orthogonal polynomials and quadratures.
An Addition Theorem for Some q-Hahn Polynomials.
An algebra of integral operators.
An Algebraic Approach to Discrete Dilations. Application to Discrete Wavelet Transforms.
An algebraic construction of discrete wavelet transforms
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.
An algorithm for nonharmonic signal analysis using Dirichlet series on convex polygons.
An Almost Orthogonal Radial Wavelet Expansion for Radial Distributions.
An application of two-parameter martingales in harmonic analysis
Some duality results and some inequalities are proved for two-parameter Vilenkin martingales, for Fourier backwards martingales and for Vilenkin and Fourier coefficients.
An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials.
An example of nonsymmetric semi-classical form of class ; generalization of a case of Jacobi sequence.
An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids
Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many...