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A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L((−1, 1), |x| dx). This orthonormal system is a generalization of the classical exponential system defining Fourier series.

- WHOSE HANKEL, Juan Luis Varona
- 2004

1991 Mathematics Subject Classification: Primary 42C10; Secondary 44A05.

Let Jμ denote the Bessel function of order μ. The functions xJα+β+2n+1(x 1/2), n = 0, 1, 2, . . . , form an orthogonal system in L2((0,∞), xα+βdx) 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 Lp((0,∞), xαdx)-norm. Also, we describe the space in which the span of… (More)

- Antonio J. Durán Guardeño, Mario Pérez, Juan Luis Varona
- ArXiv
- 2013

Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of matrices of integer numbers: not only it computes the determinants wrongly, but also it produces different results if one… (More)

- Luis M. Navas, Francisco J. Ruiz, Juan Luis Varona
- Math. Comput.
- 2012

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x;λ) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze… (More)

We prove two-weight norm inequalities for Cesàro means of generalized Hermite polynomial series and for the supremum of these means. A result about weak boundedness and an almost everywhere convergence result are also obtained.

- José J. Guadalupe, Mario Pérez, Francisco J. Ruiz, Juan Luis Varona
- 2004

Abstract. General expressions are found for the orthonormal polynomials and the kernels relative to measures on the real line of the form μ+Mδc, in terms of those of the measures dμ and (x−c)dμ. In particular, these relations allow us to obtain that Nevai’s class M(0, 1) is closed for adding a mass point, as well as several bounds for the polynomials and… (More)

- José Manuel Gutiérrez Jiménez, Ángel Alberto Magreñán, Juan Luis Varona
- Applied Mathematics and Computation
- 2011

In this paper we introduce a process we have called “Gauss-Seidelization” for solving nonlinear equations. We have used this name because the process is inspired by the well-known Gauss-Seidel method to numerically solve a system of linear equations. Together with some convergence results, we present several numerical experiments in order to emphasize how… (More)

- Luis M. Navas, Francisco J. Ruiz, Juan Luis Varona
- Journal of Approximation Theory
- 2011

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner. In addition, applying the technique of Möbius inversion from analytic number theory to Fourier expansions, we derive… (More)

- J. J. GUADALUPE, M. Amparo Escortell Pérez, Francisco J. Ruiz, Juan Luis Varona
- 2010

We study some problems related to convergence and divergence a.e. for Fourier series in systems {(pk} , where {(¡>k} is either a system of orthonormal polynomials with respect to a measure dp on [-1, 1] or a Bessel system on [0,1]. We obtain boundedness in weighted LP spaces for the maximal operators associated to Fourier-Jacobi and Fourier-Bessel series.… (More)