-function with complex parameters. I: Existence.
-function with complex parameters. II: Evaluation.
Hankel type integral transforms connected with the hyper-Bessel differential operators
In this paper we give a solution of a problem posed by the second author in her book, namely, to find symmetrical integral transforms of Fourier type, generalizing the cos-Fourier (sin-Fourier) transform and the Hankel transform, and suitable for dealing with the hyper-Bessel differential operators of order m>1 , β>0, , j=1,...,m. We obtain such integral transforms corresponding to hyper-Bessel operators of even order 2m and belonging to the class of the Mellin convolution type transforms...
Hardy and Cowling-Price theorems for a Cherednik type operator on the real line
This paper is aimed to establish Hardy and Cowling-Price type theorems for the Fourier transform tied to a generalized Cherednik operator on the real line.
Hardy spaces on SU(2)
Hardy-type inequalities for Hermite expansions.
Harmonic analysis and Radon transforms on pencils of geodesics.
Harmonic analysis for spinors on real hyperbolic spaces
We develop the L² harmonic analysis for (Dirac) spinors on the real hyperbolic space Hⁿ(ℝ) and give the analogue of the classical notions and results known for functions and differential forms: we investigate the Poisson transform, spherical function theory, spherical Fourier transform and Fourier transform. Very explicit expressions and statements are obtained by reduction to Jacobi analysis on L²(ℝ). As applications, we describe the exact spectrum of the Dirac operator, study the Abel transform...
Harmonic Analysis for Vector Fields on Hyperbolic Spaces.
Harmonic Bergman kernel for some balls.
Heat Conduction And H-Function
Hecke algebras and hypergeometric functions.
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.
Higher monotonicity properties of certain Sturm-Liouville functions