Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and computer systems. We contribute to this technique in this paper by extending our recently developed variant of the Laguerre method for numerically inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional i...

Abstract. In our previous papers [1, 2] we studied Laguerre functions and polynomials on symmetric cones Ω = H/L. The Laguerre functions l n , n ∈ Λ, form an orthogonal basis in L(Ω, dμν ) and are related via the Laplace transform to an orthogonal set in the representation space of a highest weight representations (πν ,Hν) of the automorphism group G corresponding to a tube domain T (Ω). In thi...

The continuous-time implementation of the popular transversal filter is problematic since it is impossible to implement an ideal time delay in continuous-time hardware. We believe that building an ideal time delay would not be worthwhile anyway since the ideal time delay has shown to be inferior to low-pass (Gamma) and all-pass (Laguerre) stages in discrete-time simulations. We demonstrate feed...

We demonstrate electromagnetically induced transparency with the control laser in a Laguerre–Gaussian mode. The transmission spectrum is studied in an ultracold gas for the D2 line in both Rb and Rb, where the decoherence due to diffusion of the atomic medium is negligible. We compare these results to a similar configuration, but with the control laser in the fundamental laser mode. We model th...

Abstract. This paper discusses a method based on Laguerre polynomials combined with a Filtered Conjugate Residual (FCR) framework to compute the product of the exponential of a matrix by a vector. The method implicitly uses an expansion of the exponential function in a series of orthogonal Laguerre polynomials, much like existing methods based on Chebyshev polynomials do. Owing to the fact that...

The author studies the uniform convergence of extended Lagrange interpolation processes based on the zeros of Generalized Laguerre polynomials. 2009 Elsevier Inc. All rights reserved.

Many limits are known for hypergeometric orthogonal polynomials that occur in the Askey scheme. We show how asymptotic representations can be derived by using the generating functions of the polynomials. For example, we discuss the asymptotic representation of the Meixner-Pollaczek, Jacobi, Meixner, and Krawtchouk polynomials in terms of Laguerre polynomials.

In this paper, a new two dimensional (2D) adaptive filter structure is developed. It is based on modeling the impulse response of the 2D IIR systems as a finite linear combination of a set of 2D Laguerre orthonormal functions. When long impulse response system is required to identify, computer simulation shows that the 2D Laguerre filter has better performance than the conventional 2D FIR filte...

The article deals with the relationship between Laguerre geometry and Minkowski sum. This relationship is used to create new geometry based generally on fundamental objects different to closed balls that formed Laguerre geometry. In the end of the article, there is defined also generalization of medial axis transform to the newly defined spaces and proved its uniqueness. The article continues t...

The aim of this paper is to carry out a rigorous error analysis for the Strang splitting Laguerre–Hermite/Hermite collocation methods for the time-dependent Gross–Pitaevskii equation (GPE). We derive error estimates for full discretizations of the three-dimensional GPE with cylindrical symmetry by the Strang splitting Laguerre–Hermite collocation method, and for the d-dimensional GPE by the Str...