Rearrangements of periodic multiplicative orthogonal series
Recent developments in the theory of Haar series
Recent developments in the theory of Walsh series.
Recurrence relations for the coefficients of expansions in classical orthogonal polynomials of a discrete variable
A method is given to find a recurrence relation for the coefficients of the series expansion of a function f with respect to classical orthogonal polynomials of a discrete variable, which follows from a linear difference equation satisfied by f.
Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials
Let be any sequence of classical orthogonal polynomials. Further, let f be a function satisfying a linear differential equation with polynomial coefficients. We give an algorithm to construct, in a compact form, a recurrence relation satisfied by the coefficients in . A systematic use of the basic properties (including some nonstandard ones) of the polynomials results in obtaining a low order of the recurrence.
Relations between some classes of functions of generalized bounded variation
We prove inclusion relations between generalizing Waterman's and generalized Wiener's classes for functions of two variable.
Representation of product systems on the interval .
Results on spline-Fourier and Ciesielski-Fourier series
Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and θ-summability, strong summability and multipliers. The connection between Fourier series...
Riesz summability of multiple Hermite series in Lp spaces.
Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
We propose a definition of Riesz transforms associated to the Ornstein-Uhlenbeck operator based on the Dunkl Laplacian. In the case related to the group ℤ ₂ it is proved that the Riesz transform is bounded on the corresponding spaces, 1 < p < ∞.