Let f be a real entire function with finitely many non-real zeros, not of the form f = Ph with P a polynomial and h in the Laguerre-Pólya class. Lower bounds are given for the number of non-real zeros of f ′′ + ωf , where ω is a positive real constant.

The relationship between the mode content and the fractional Fourier and fractional Hankel transforms of a function is established. It is shown that the Laguerre-Gauss spectrum of a rotationally symmetric wave front can be determined from the wave front's fractional Hankel transforms taken at the optical axis.

A robust technique is presented for parametric identification of linear time-invariant systems in the time domain. Based on a Sanathanan-Koerner iteration, the transfer function coefficients are calculated iteratively by minimizing a weighted linear cost function. The time-domain equivalent of the Muntz-Laguerre basis is used to improve the numerical conditioning of the associated system equati...

Pressing questions in cosmology such as the nature of dark matter and dark energy can be addressed using large galaxy surveys, which measure the positions, properties and redshifts of galaxies in order to map the large-scale structure of the Universe. We review the Fourier-Laguerre transform, a novel transform in 3D spherical coordinates which is based on spherical harmonics combined with dampe...

We consider ensembles of Gaussian (Hermite) and Wishart (Laguerre) N ×N hermitian matrices. We study the effect of finite rank perturbations of these ensembles by a source term. The rank r of the perturbation corresponds to the number of non-null eigenvalues of the source matrix. In the perturbed ensembles, the correlation functions can be written in terms of kernels. We show that for all N , t...

A Laguerre tessellation is a generalization of a Voronoi tessellation where the proximity between points is measured via a power distance rather than the Euclidean distance. Laguerre tessellations have found significant applications in materials science, providing improved modeling of (poly)crystalline microstructures and grain growth. There exist efficient algorithms to construct Laguerre tess...

A mesh M with planar faces is called an edge offset (EO) mesh if there exists a combinatorially equivalent mesh M d such that corresponding edges of M and M d lie on parallel lines of constant distance d. The edges emanating from a vertex of M lie on a right circular cone. Viewing M as set of these vertex cones, we show that the image of M under any Laguerre transformation is again an EO mesh. ...

The transformation of a Laguerre series f (z) = ∑n=0 λ (α) n L (α) n (z) to a power series f (z) = ∑n=0 γnz n is discussed. Since many nonanalytic functions can be expanded in terms of generalized Laguerre polynomials, success is not guaranteed and such a transformation can easily lead to a mathematically meaningless expansion containing power series coefficients that are infinite in magnitude....

Abstract. The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite rank random matrices is found in terms of a Painlevé V system, and the solution of its associated linear isomonodromic system. In particular it is characterised by the polynomial solutions to the isomonodromic equations which are also orthogonal with respect to a deformation of the La...

We show combinatorially that the higher-order matching polynomials of several families of graphs are d-orthogonal polynomials. The matching polynomial of a graph is a generating function for coverings of a graph by disjoint edges; the higher-order matching polynomial corresponds to coverings by paths. Several families of classical orthogonal polynomials—the Chebyshev, Hermite, and Laguerre poly...