The solution for multi-frequency plane waves propagating through a dissipative and nonlinear medium is shown for some examples of periodic conditions. The expression may for any given condition be expressed analytically as a ratio of Fourier series with Bessel function coefficients. In the examples are shown how the final appearance of any initial wave always is a pure periodic wave in the lowe...

Let Jμ denote the Bessel function of order μ. The functions x−α−1Jα+2n+1(x), n = 0, 1, 2, . . . , form an orthogonal system in the space L2((0,∞), x2α+1dx) when α > −1. In this paper we prove that the Fourier series associated to this system is of restricted weak type for the endpoints of the interval of mean convergence, while it is not of weak type if α ≥ 0.

Our objective in this survey is to present some results concerning to transference of multipliers, maximal multipliers and transplantation operators between Fourier-Bessel series and Hankel integrals. Also we list some related problems that can be interesting and that have not been studied yet. From August 31st to September 3rd, 2004, was held in Merlo (San Luis, Argentine) the congress ”VII En...

A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...

1. Introduction Recently [2,3] we found necessary and sufficient conditions for the convergence at a preassigned point of the spherical partial sums of the Fourier integral in a class of piece-wise smooth functions in Euclidean space. These yield elementary examples of divergent Fourier integrals in three dimensions and higher. Meanwhile, several years ago Gottlieb and Orsag[1] observed that in...

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined Fourier–Bessel series transforms, respectively. Their equivalent relation shown, which the upper bound estimate for best RKHS provided. The convergence rate bounded modulus smoothness, shows that can attain sa...