Elasticity for integral-valued polynomials

Extension of Vector-valued Integral Polynomials

We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they...

Integral inequalities for algebraic polynomials

In this paper we consider two extremal problems for algebraic polynomials in L 2 metrics. (1) Let Pn be the class of all algebraic polynomials P(x) = akxk of degree at most nand IJPllda= (fIR IP(x)1 2 da(x))1/2, where da(x) is a nonnegative measure on lit We determine the best constant in the inequality lakl:::; Cn,k(da)IJPl!da-, for k = O,l, ... ,n, when P E Pn and such that = 0, k = 1, ... ,m...

Vector Valued Macdonald Polynomials

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type AN−1. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and t...

Integer-valued Polynomials

Let R be a Krull ring with quotient field K and a1, . . . , an in R. If and only if the ai are pairwise incongruent mod every height 1 prime ideal of infinite index in R does there exist for all values b1, . . . , bn in R an interpolating integer-valued polynomial, i.e., an f ∈ K[x] with f(ai) = bi and f(R) ⊆ R. If S is an infinite subring of a discrete valuation ring Rv with quotient field K a...

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials