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24,161
Spectral Factorization of Laurent Polynomials
 Advances in Computational Mathematics
, 1997
"... . We analyse the performance of five numerical methods for factoring a Laurent polynomial, which is positive on the unit circle, as the modulus squared of a real algebraic polynomial. It is found that there is a wide disparity between the methods, and all but one of the methods are significantly inf ..."
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Cited by 20 (1 self)
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. We analyse the performance of five numerical methods for factoring a Laurent polynomial, which is positive on the unit circle, as the modulus squared of a real algebraic polynomial. It is found that there is a wide disparity between the methods, and all but one of the methods are significantly
LAURENT POLYNOMIALS AND EULERIAN NUMBERS
, 908
"... ABSTRACT. Duistermaat and van der Kallen show that there is no nontrivial complex Laurent polynomial all of whose powers have a zero constant term. Inspired by this, Sturmfels posed two questions: Do the constant terms of a generic Laurent polynomial form a regular sequence? If so, then what is the ..."
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Cited by 1 (0 self)
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ABSTRACT. Duistermaat and van der Kallen show that there is no nontrivial complex Laurent polynomial all of whose powers have a zero constant term. Inspired by this, Sturmfels posed two questions: Do the constant terms of a generic Laurent polynomial form a regular sequence? If so, then what
Decompositions of Laurent polynomials
"... Abstract. 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 e ..."
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Cited by 4 (0 self)
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effort by Ritt and others, little progress has been made towards solving the analogous problem for rational functions. In this paper we use results of Avanzi–Zannier and Bilu–Tichy to prove analogues of Ritt’s results for decompositions of Laurent polynomials, i.e., rational functions with denominator x
Generic rigidity of Laurent polynomials
"... Abstract. Tadic Lfunctions associated to Laurent polynomials f are introduced. They interpolate Lfunctions of p mpower order exponential sums associated to f for all positive m. The rigidity of f is also introduced. The Newton polygons of Lfunctions of p mpower order exponential sums associate ..."
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Abstract. Tadic Lfunctions associated to Laurent polynomials f are introduced. They interpolate Lfunctions of p mpower order exponential sums associated to f for all positive m. The rigidity of f is also introduced. The Newton polygons of Lfunctions of p mpower order exponential sums
Monotonicity Of Zeros Of Orthogonal Laurent Polynomials
"... Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the HellmanFeynman theorem are also extended to a mono ..."
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Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the HellmanFeynman theorem are also extended to a
Algorithms for the Functional Decomposition of Laurent Polynomials
"... Abstract. Recent work has detailed the conditions under which univariate Laurent polynomials have functional decompositions. This paper presents algorithms to compute such univariate Laurent polynomial decompositions efficiently and gives their multivariate generalization. One application of functio ..."
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Cited by 2 (0 self)
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Abstract. Recent work has detailed the conditions under which univariate Laurent polynomials have functional decompositions. This paper presents algorithms to compute such univariate Laurent polynomial decompositions efficiently and gives their multivariate generalization. One application
Convergence of Interpolating Laurent Polynomials on an Annulus
"... . We study the convergence of Laurent polynomials that interpolate functions on the boundary of a circular annulus. The points of interpolation are chosen to be uniformly distributed on the two circles of the boundary. A maximal convergence theorem for functions analytic on the closure of the annulu ..."
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. We study the convergence of Laurent polynomials that interpolate functions on the boundary of a circular annulus. The points of interpolation are chosen to be uniformly distributed on the two circles of the boundary. A maximal convergence theorem for functions analytic on the closure
Undecidability in Matrices over Laurent Polynomials
, 2004
"... We show that it is undecidable for finite sets S of upper triangular 4 × 4matrices over Z[x, x −1] whether or not all elements in the semigroup generated by S have a nonzero constant term in some of the Laurent polynomials of the first row. This result follows from a representations of the integer ..."
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We show that it is undecidable for finite sets S of upper triangular 4 × 4matrices over Z[x, x −1] whether or not all elements in the semigroup generated by S have a nonzero constant term in some of the Laurent polynomials of the first row. This result follows from a representations of the integer
Factorization of multivariate positive Laurent polynomials
 J. APPROX. THEORY
, 2005
"... 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 FéjerRiesz theorem. Then we discuss a computational metho ..."
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Cited by 6 (2 self)
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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 FéjerRiesz theorem. Then we discuss a computational
PRIME AND COMPOSITE LAURENT POLYNOMIALS
, 710
"... Abstract. In his paper [15] Ritt constructed a decomposition theory of polynomials and described explicitly polynomial solutions of the functional equation f(p(z)) = g(q(z)). In this paper we construct a selfcontained decomposition theory of rational functions with at most two poles. In particular ..."
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Cited by 12 (5 self)
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Abstract. In his paper [15] Ritt constructed a decomposition theory of polynomials and described explicitly polynomial solutions of the functional equation f(p(z)) = g(q(z)). In this paper we construct a selfcontained decomposition theory of rational functions with at most two poles
Results 1  10
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24,161