Methods approaching the problem of the Hermite Birkhoff interpolation of scattered data by combining Shepard operators with local interpolating polynomials are not new in literature [1–4]. In [3] combinations of Shepard operators with bivariate Hermite-Birkhoff local interpolating polynomials are introduced to increase the algebraic degree of precision (polynomial reproduction degree) of Shepar...

We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the viewpoint of convex optimization. We relate the question to sums of squares decompositions of a certain Hermite matrix. If some power of a polynomial admits a de...

We show combinatorially that the higher-order matching polynomials of several families of graphs are d-orthogonal polynomials. The matching polynomial of a graph is a generating function for coverings of a graph by disjoint edges; the higher-order matching polynomial corresponds to coverings by paths. Several families of classical orthogonal polynomials—the Chebyshev, Hermite, and Laguerre poly...

The strong asymptotic behaviour of orthogonal polynomials with respect to a general class of varying measures is given for the case of the unit circle and the real line. These results are used to obtain certain asymptotic relations for the polynomials involved in the construction of Hermite–Pad e approximants of a Nikishin system of functions. c © 1998 Elsevier Science B.V. All rights reserved....

In this paper, we introduce a novel signal shaping approach for multi−carrier systems. We propose to combine Hermite functions in order to get a good time−frequency localization property for multi−carrier signals, which is important for robustness against the time−frequency dispersion of the wireless channel. In our work, we orthogonalize the linear combination of Hermite functions in order to ...

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven...

We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special symmetric generalizations of the Hermite polynomials.

Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The best-known example of this type is the Hermite functions, i.e., the Hermite polynomials multiplied by exp(−x2/2), which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a com...

Results on multiple orthogonal polynomials will be surveyed. Multiple orthogonal polynomials are intimately related to Hermite–Pad e approximants and often they are also called Hermite–Pad e polynomials. Special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials, referred to as Angel...

Fractal interpolation techniques provide good deterministic representations of complex phenomena. This paper approaches the Hermite interpolation using fractal procedures. This problem prescribes at each support abscissa not only the value of a function but also its first p derivatives. It is shown here that the proposed fractal interpolation function and its first p derivatives are good approx...