Results 91 to 100 of about 522,796 (288)
Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states [PDF]
, 2012 We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic $L^2$-spaces. Using these polynomials, we then define regular and anti-regular subspaces of these $L^2$-spaces, the associated reproducing ...
arxiv +1 more source
A Note on the (p, q)-Hermite Polynomials
, 2018 In this paper, we introduce a new generalization of the Hermite polynomials via (p; q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence ...
U. Duran, M. Acikgoz, A. Esi, S. Araci
semanticscholar +1 more source
Finite sums and generalized forms of Bernoulli polynomials [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1999 We introduce new classes of Bernoulli polynomials, useful to evaluate partial sums of Hermite and Laguerre polynomials. We also comment on the possibility of extending the class of Bernoulli numbers itself, and indicate their importance in the derivation
G. Dattoli, S. Lorenzutta, C. Cesarano
doaj
On the hermite matrix of a polynomial
Linear Algebra and its Applications, 1971 AbstractWe investigate the location of the eigenvalues of the Hermite matrix of a given complex polynomial, the question under what conditions a given polynomial and the characteristic polynomial of its Hermite matrix are identical, and the question under what conditions the Hermite matrix has only one distinct eigenvalue.
openaire +2 more sources
Multi‐Slit Diffraction in Scaled Space‐Time
Natural Sciences, EarlyView.A space‐time scaling is used to transform quantum wave packets describing free particle motion to packets moving in an effective harmonic oscillator potential that confines and directs the wave fronts along the classical phase space of the oscillator. The transformation is applied to multi‐slit diffraction and shown to characterize diffraction features
James M. Feagin
wiley +1 more source
Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials
Journal of Applied Mathematics, 2013 Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher
Hee Sun Jung, Ryozi Sakai
doaj +1 more source
On the complex Hermite polynomials
Filomat, 2020 In this paper we use a set of partial differential equations to prove an expansion theorem for multiple complex Hermite polynomials. This expansion theorem allows us to develop a systematic and completely new approach to the complex Hermite polynomials.
openaire +2 more sources
Irreducibility of generalized Hermite-Laguerre Polynomials II [PDF]
, 2013 In this paper, we show that for each $n\geq 1$, the generalised Hermite-Laguerre Polynomials $G_{\frac{1}{4}}$ and $G_{\frac{3}{4}}$ are either irreducible or linear polynomial times an irreducible polynomial of degree $n-1$.
arxiv +1 more source
Quantum Ghost Imaging by Sparse Spatial Mode Reconstruction
Advanced Quantum Technologies, EarlyView.Hermite–Gaussian spatial modes are used in quantum ghost imaging for enhanced image reconstruction, by exploiting modal sparsity. By leveraging structured light as a basis for imaging, time‐efficient and high resolution quantum ghost imaging is achieved, paving the way for breakthroughs in low‐light, biological science applications.
Fazilah Nothlawala +4 more
wiley +1 more source
DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER WITH ORTHOGONAL POLYNOMIAL SOLUTIONS
Pesquimat, 2014 In this paper we developed conditions for orthogonality of polynomial Solutions of the fourth order differential equations with polynomial coefficients.
Santiago César Rojas Romero
doaj +1 more source