We compute the integrals of products of Hermite functions using the generating functions. The precise asymptotics of products of 4 Hermite functions are presented below. This estimate is relevant for the corresponding cubic nonlinear equation.

We obtain several formulas for the action of the bilinear Hilbert transform on pairs of Hermite and Laguerre functions. The result can be expressed as a linear combination of products of Hermite or Laguerre functions.

Expansion of a random function in terms of an orthogonal random base was introduced by Cameron and Martin [1] and Wiener [2], Meecham and Siegel [3] and Meecham and Jeng [4] applied this technique to the problem of hydrodynamic turbulence. Recently, Jahedi and Ahmadi [5] used it in their study of nonlinear structures subjected to random loads. The technique is now well known as the Wiener-Hermi...

Interpolatory and non-interpolatory multivariate Hermite type subdivision schemes are introduced in [8, 7]. In their applications in free-form surfaces, symmetry properties play a fundamental role: one can essentially argue that a subdivision scheme without a symmetry property simply cannot be used for the purpose of modelling free-form surfaces. The symmetry properties defined in the article [...

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.

Multiwavelets are generated from refinable function vectors by using multiresolution analysis. In this paper we investigate the approximation properties of a multivariate refinable function vector associated with a general dilation matrix in terms of both the subdivision operator and the order of sum rules satisfied by the matrix refinement mask. Based on a fact about the sum rules of biorthogo...

We establish some estimates of the right-hand side of Hermite-Hadamard type inequalities for functions whose derivatives absolute values are harmonically s-convex. Several Hermite-Hadamard type inequalities for products of two harmonically s-convex functions are also considered.

This work is intended to give some ideas to extract motion information from an image sequence. A directional energy is defined in terms of the 1-D Hermite transform coefficients of local projections. Each projection is described by the Hermite transform resulting in a directional derivative analysis of the input at a given scale. Gaussian-derivative operators have long been used in computer vis...

Hermite spectral methods are investigated for linear diffusion equations and the viscous Burgers’ equation in unbounded domains. When the solution domain is unbounded, the diffusion operator no longer has a compact resolvent, which makes the Hermite spectral methods unstable. To overcome this difficulty, a time-dependent scaling factor is employed in the Hermite expansions, which yields a posit...