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Pencils of lines in generalized Laguerre spaces
Combinatorics Multidimensional Laguerre spaces subspaces pencils Grassmann spaces
2012/4/17
In the paper we characterize subspaces and pencils of lines of generalized (and multidimensional) Laguerre spaces and we consider definability of the structure of "conic" pencils in the Grassmann spac...
A heat kernel version of Hardy's theorem for the Laguerre hypergroup
Laguerre hypergroup Uncertainty principle Hardy's theorem
2011/9/30
The uncertainty principle says that a function and its Fourier transform can't simultaneously decay very rapidly at infinity. A classical version of uncertainty principle, known as Hardy's theorem, wa...
A heat kernel version of Hardy's theorem for the Laguerre hypergroup
Laguerre hypergroup Uncertainty principle Hardy's theorem
2011/9/29
The uncertainty principle says that a function and its Fourier transform can't simultaneously decay very rapidly at infinity. A classical version of uncertainty principle, known as Hardy's theorem, wa...
Higher order Laguerre-Gauss mode degeneracy in realistic, high finesse cavities
Higher order Laguerre-Gauss degeneracy realistic high finesse cavities
2011/10/14
Higher order Laguerre-Gauss (LG) beams have been proposed for use in future gravitational wave detectors, such as upgrades to the Advanced LIGO detectors and the Einstein Telescope, for their potentia...
Krall-Laguerre commutative algebras of ordinary differential operators
Krall-Laguerre commutative algebras ordinary differential operators Classical Analysis and ODEs
2011/9/15
Abstract: In 1999, Grunbaum, Haine and Horozov defined a large family of commutative algebras of ordinary differential operators which have orthogonal polynomials as eigenfunctions. These polynomials ...
Discrete Laguerre-Sobolev expansions: A Cohen type inequality
Laguerre polynomials Laguerre–Sobolev type polynomials Cohen type inequality Bessel functions
2011/8/25
Abstract: C. Markett proved a Cohen type inequality for the classical Laguerre expansions in the appropriate weighted $L^{p}$ spaces. In this paper, we get a Cohen type inequality for the Fourier expa...
Bose-Einstein condensation transition studies for atoms confined in Laguerre-Gaussian laser modes
Bose-Einstein condensation transition atoms Laguerre-Gaussian laser modes Atomic Physics
2011/8/1
Abstract: Multiply-connected traps for cold, neutral atoms fix vortex cores of quantum gases. Laguerre-Gaussian laser modes are ideal for such traps due to their phase stability. We report theoretical...
Bose-Einstein condensation transition studies for atoms confined in Laguerre-Gaussian laser modes
Bose-Einstein condensation transition atoms Laguerre-Gaussian laser modes Atomic Physics
2011/8/1
Abstract: Multiply-connected traps for cold, neutral atoms fix vortex cores of quantum gases. Laguerre-Gaussian laser modes are ideal for such traps due to their phase stability. We report theoretical...
Subordination by orthogonal martingales in $L^{p}$ and zeros of Laguerre polynomials
orthogonal martingales $L^{p}$ zeros of Laguerre polynomials
2011/1/18
In this paper we address the question of finding the best Lp-norm constant for martingale transforms with one-sided orthogonality. Let O = (,B, P)be a probability space with filtration B generated by ...
The application of the pseudostate-close-coupling method using a non-orthogonal Laguerre-L^2 basis for electron-helium scattering
Differential and total cross sections Elastic and excitation
2010/9/25
Differential and total cross sections for elastic and excitation from the ground state to n ≤ 2 states of atomic helium by electrons are computed for incident energies in the range from 5 to 50 eV. Th...
A Laguerre minimal surface is an immersed surface in the Euclidean space being an extremal of the functional \int (H^2/K - 1) dA. In the present paper, we prove that the only ruled Laguerre minimal s...
On Lusin's area integrals and g-functions in certain Dunkl and Laguerre settings
On Lusin's area integrals g-functions Laguerre settings
2010/11/9
We investigate $g$-functions and Lusin's area type integrals related to certain multi-dimensional Dunkl and Laguerre settings. We prove that the considered square functions are bounded on weighted $L^...
Fraunhofer diffraction of a Laguerre-Gaussian laser beam by fork-shaped grating
Fraunhofer diffraction Laguerre-Gaussian laser beam fork-shaped grating
2010/11/17
In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by diffractive grating with embe...
Minimal representations of conformal groups and generalized Laguerre functions
Minimal representations conformal groups generalized Laguerre functions
2010/12/10
We give a unified construction of the minimal representation of a finite cover G of the conformal group of a (non necessarily euclidean) Jordan algebra V . This representation is realized on the L2-sp...
Direct spreading measures of Laguerre polynomials
Orthogonal polynomials Laguerre polynomials spreading lengths
2010/11/26
The direct spreading measures of the Laguerre polynomials L( )n (x), which quantify the distribution of its Rakhmanov probability density n, (x) = 1 d2 n x e−x h L( ) n (x)
i2 along the positi...