منابع مشابه
Orthogonal Laurent Polynomials of Jacobi, Hermite and Laguerre Types
We will outline in this paper a general procedure for constructing whole systems of orthogonal Laurent polynomials on the real line from systems of orthogonal polynomials. To further explain our intentions, we proceed with some basic definitions and results, all of which appear, or are modifications of those that appear, in the literature. In particular, [1,2,3,4,5,6,7,8,9,10,11,12] were consul...
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In the 1920’s, Ritt studied the operation of functional composition g ◦ h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which a polynomial can have multiple ‘prime factorizations’ with respect to this operation. Despite significant effort by Ritt and others, little progress has been made towards solving the analogous problem for rational fu...
متن کاملMultivariate Positive Laurent Polynomials
Recently Dritschel proves that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dritschel theorem. Our proof is based on the univariate matrix Féjer-Riesz theorem. Then we discuss a computational method to find approximates of polynomial matrix factorization. Some numerical examples will be shown. F...
متن کاملGeneric Exponential Sums Associated to Laurent Polynomials in One Variable
We shall determine the generic Newton polygon of L-functions of exponential sums associated to Laurent polynomials in one variable. Throughout this paper, p denotes a prime number, and q denotes a power of p. Write Fp := Z/pZ. Let F̄p be a fixed algebraic closure of the finite field Fp, and Fq the finite field with q elements in F̄p. Let f be a Laurent polynomial over Fq. We assume that the leadi...
متن کاملLaurent Polynomials and Superintegrable Maps
This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author’s recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 recurrences, and on the Laurent property. Subsequently a family of fourth-order recurrences that share the Laurent property are considered, which a...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1990
ISSN: 0377-0427
DOI: 10.1016/0377-0427(90)90424-x