Determinant representations of Appell polynomial sequences

On Appell sequences of polynomials of Bernoulli and Euler type

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number theoretical properties. A class of Euler-type polynomials is also presented. © 2007 Elsevier Inc. All rights reserved.

Appell Sequences, Continuous Wavelet Transforms and Series Expansions

A series expansion with remainder for functions in a Sobolev space is derived in terms of the classical Bernoulli polynomials, the B-spline scale-space and the continuous wavelet transforms with the derivatives of the standardized B-splines as mother wavelets. In the limit as their orders tend to infinity, the B-splines and their derivatives converge to the Gaussian function and its derivatives...

Polynomial Surface Patch Representations

Uniqueness of Polynomial Canonical Representations

Abstract. Let P (z) and Q(y) be polynomials of the same degree k ≥ 1 in the complex variables z and y, respectively. In this extended abstract we study the non-linear functional equation P (z) = Q(y(z)), where y(z) is restricted to be analytic in a neighborhood of z = 0. We provide sufficient conditions to ensure that all the roots of Q(y) are contained within the range of y(z) as well as to ha...

Equivariant Polynomial Automorphisms of -representations

We show that every equivariant polynomial automorphism of a-representation and of the reduction of an irreducible-representation is a multiple of the identity.