Utilizing early time response and low-frequency data, the complete electromagnetic response of a threedimensional conducting structure is generated. By using mutually complementary data, simultaneous extrapolation in time and frequency domains are carried out. This is performed through the use of the associated Hermite polynomials. The interesting property of the Hermite polynomials is that the...

We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...

We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our construction of the discrete Lagrangian adopts Hermite interpolation polynomials and the Euler–Maclaurin quadrature formula, and involves applying collocation...

We study the weak and strong type boundedness of maximal heat–diffusion operators associated with the system of generalized Hermite polynomials and with two different systems of generalized Hermite functions. We also give a necessary background to define Sobolev spaces in this context.

We study the variation of the zeros of the Hermite function Hλ(t) with respect to the positive real variable λ. We show that, for each nonnegative integer n, Hλ(t) has exactly n + 1 real zeros when n < λ ≤ n + 1 and that each zero increases from −∞ to ∞ as λ increases. We establish a formula for the derivative of a zero with respect to the parameter λ; this derivative is a completely monotonic ...

We study the structure of solutions of the one-dimensional non-linear pseudodifferential equation describing the dynamics of the p-adic open string for the scalar tachyon field p 1 2 ∂ t Φ = Φ. We elicit the role of real zeros of the entire function Φ(z) and the behaviour of solutions Φ(t) in the neighbourhood of these zeros. We point out that discontinuous solutions can appear if p is even. We...

The relativistic Hermite polynomials (RHP) were introduced in 1991 by Aldaya et al. [3] in a generalization of the theory of the quantum harmonic oscillator to the relativistic context. These polynomials were later related to the more classical Gegenbauer (or more generally Jacobi) polynomials in a study by Nagel [4]. For this reason, they do not deserve any special study since their properties...