Learn More
Let Jµ denote the Bessel function of order µ. The functions x −α/2−β/2−1/2 J α+β+2n+1 (x 1/2), n = 0, 1, 2,. .. , form an orthogonal system in L 2 ((0, ∞), x α+β dx) when α + β > −1. In this paper we analyze the range of p, α and β for which the Fourier series with respect to this system converges in the L p ((0, ∞), x α dx)-norm. Also, we describe the(More)
In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and un-weighted inequalities in the spaces L p ((0, 1), x 2ν+1 dx). Moreover, weak and restricted weak type inequalities are obtained for the critical(More)
We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann type series as special cases. Concerning applications, several new results are obtained. From the Dunkl analogue of(More)
For most orthogonal systems and their corresponding Fourier series, the study of the almost everywhere convergence for functions in L p requires very complicated research, harder than in the case of the mean convergence. For instance, for trigonometric series, the almost everywhere convergence for functions in L 2 is the celebrated Carleson theorem, proved(More)