Let a > 0 be the least upper bound of y for which f(z) 0(e-°My) for some positive constant q as |z| -+ o» on the real axis. It is then proved that at least an infinite subsequence of the coefficients \an} in oo f(z) = e-z2/2 £ anHn(z), n=0 where the Hn are the normalized Hermite polynomials, must satisfy certain lower bounds. The theorems show two striking facts. First, the convergence rate of ...

In order to improve estimation accuracy of nonliear system with linear measurement model, simplified gauss hermite filter based on sparse grid gauss hermite quadrature (SGHF) is proposed. Comparing to conventional Gauss-Hermite filter (GHF) based on tensor product gauss quadrature rule, simplified SGHF not only maintains GHF’s advantage of precission controllable, high estimation accuracy, but ...

A methodology for image fusion based on the Hermite transform is presented. First, we demonstrate fusion with multispectral images from the same satellite (Landsat 7 ETM+) with different spatial resolutions. In this case we show how the proposed method can help improve spatial resolution. In the second case we show fusion with different sensor images, namely SAR and multispectral Landsat 5 TM. ...

For prescribed values of a function and its partial derivatives of orders 1 and 2 at the vertices of a square, we fit an interpolating surface. We investigate two families of solutions provided by two Hermite subdivision schemes, denoted HD2 and HR2. Both schemes depend on 2 matrix parameters, a square matrix of order 2 and a square matrix of order 3. We exhibit the masks of both schemes. We co...

The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by Gröchenig and Lyubarskii in Gabor frames with Hermite functions, C. R. Acad. Sci. Paris, Ser. I 344 157-162 (2007). Building on Seip ́s work Beurling type density...

Piecewise Hermite cubics have been widely used in a variety of ways for solving partial differential equations. For a number of these techniques, knowledge about the Hermite cubic collocation approximations to the spectrum of the Laplace operator is often very useful, for error analysis and, a fortiori, possible iteration parameters. To this end, we givc here explicit closed-form expressions fo...

We present a symbolic algorithm generating finite-element schemes with interpolating Hermite polynomials intended for solving the boundary-value problems with self-adjoint second-order differential equation and implemented in the Maple computer algebra system. Recurrence relations for the calculation in analytical form of the interpolating Hermite polynomials with nodes of arbitrary multiplicit...

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 express Wronskian Hermite polynomials in the basis and obtain an explicit formula for coefficients. From this we deduce upper bound modulus of roots case partitions length 2. also derive a general real purely imaginary roots. These bounds are very useful study irreducibility polynomials. Additionally, generalize some our results to larger class