Heisenberg uncertainty relation in quantum Liouville equation.
Heisenberg-Pauli-Weyl uncertainty principle for the Riemann-Liouville operator.
Hermite and Laguerre polynomials and matrix-valued stochastic.
Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms.
We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on Rd which may be written as P(x)exp(-(Ax,x)), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with...
Hermite martingales
Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function
AMS Subject Classification 2010: 11M26, 33C45, 42A38.Necessary and sufficient conditions for absence of zeros of ζ(s) in the half-plane σ ... Expansion of holomorphic functions in series of Hermite polynomials ...
Hermite Series with Polar Singularities
MSC 2010: 33C45, 40G05Series in Hermite polynomials with poles on the boundaries of their regions of convergence are considered.
How sharp is Bernstein's inequality for Jacobi polynomials?
Hypergeometric orthogonal systems of polynomials. I
Hypergeometric orthogonal systems of polynomials. II
Hypergeometric orthogonal systems of polynomials. III
Inequalities and identities for ... .
Inequalities for Laguerre functions.
Inequalities for the smallest zeros of Laguerre polynomials and their -analogues.
Integrability Theorems For Jacobi Series
Integral representation of orthogonal exponential polynomials
Integral representations for multiple Hermite and multiple Laguerre polynomials
We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
Integral Representations of Functional Series with Members Containing Jacobi Polynomials
MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials.
Integrals involving Gegenbauer and Hermite polynomials on the imaginary axis.
Integrals involving Hermite polynomials, generalized hypergeometric series and Fox's H-function, and Fourier-Hermite series for products of generalized hypergeometric functions
We evaluate an integral involving an Hermite polynomial, a generalized hypergeometric series and Fox's H-function, and employ it to evaluate a double integral involving Hermite polynomials, generalized hypergeometric series and the H-function. We further utilize the integral to establish a Fourier-Hermite expansion and a double Fourier-Hermite expansion for products of generalized hypergeometric functions.