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ORTHOGONAL POLYNOMIALS ON THE SIERPINSKI GASKET
Jacobi matrix Laplacian Sierpinski Gasket Orthogonal Polynomials Recursion Relation
2015/12/10
The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket (SG) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of pol...
Tropical varieties with polynomial weights and corner loci of piecewise polynomials
Tropical varieties polynomial weights corner loci of piecewise polynomials
2011/2/28
Counting Euler characteristics of the discriminant of the quadratic equation in terms of
Newton polytopes in two different ways, G. Gusev ([Gus]) found an unexpected relation for
mixed volumes of tw...
Strict Positivstellens\" atze for matrix polynomials with scalar constraints
matrix polynomials scalar constraints
2010/11/24
We extend Krivine's strict positivstellensatz for usual (real multivariate) polynomials to symmetric matrix polynomials with scalar constraints. The proof is an elementary computation with Schur compl...
On explicit factors of Cyclotomic polynomials over finite fields
Cyclotomic polynomials finite fields
2010/11/24
We study the explicit factorization of $2^n r$-th cyclotomic polynomials over finite field $\mathbb{F}_q$ where $q, r$ are odd with $(r, q) =1$. We show that all irreducible factors of $2^n r$-th cyc...
Vanishing integrals for Hall-Littlewood polynomials
Vanishing integrals Hall-Littlewood polynomials
2010/11/24
It is well known that if one integrates a Schur function indexed by a partition $\lambda$ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of $\lambda$ have even m...
Thom polynomials and the Green-Griffiths conjecture
Thom polynomials the Green-Griffiths conjecture
2010/11/24
In the first part of this paper we apply equivariant localization techniques to prove the Green-Griffiths conjecture for a generic projective hypersurface of dimension n and degree >2^{8nlogn}. In th...
Geometry of the locus of polynomials of degree 4 with iterative roots
Geometry polynomials iterative roots
2010/11/23
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
Multivariate Rogers-Szegö polynomials and flags in finite vector spaces
Multivariate Rogers-Szegö polynomials flags in finite vector spaces
2010/11/9
We give a recursion for the multivariate Rogers-Szeg\"o polynomials, along with another recursive functional equation, and apply them to compute special values. We also consider the sum of all $q$-mu...
Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields
Relatively Prime Polynomials Nonsingular Hankel Matrices
2010/11/12
The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel ma...
We study a new family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with differential operators of Dunkl-type. These polynomials ...
A "missing" family of classical orthogonal polynomials
missing family classical orthogonal polynomials
2010/11/12
We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can...
Positive trigonometric polynomials for strong stability of difference equations
trigonometric polynomials strong stability difference equations
2010/11/11
We follow a polynomial approach to analyse strong stability of linear difference equations with rationally independent delays. Upon application of the Hermite stability criterion on the discrete-time ...
Interpolation function of the genocchi type polynomials
Interpolation function the genocchi type polynomials
2010/11/17
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials...
Convergence of Bieberbach polynomials in domains with interior cusps
Bieberbach polynomials domains interior cusps
2010/10/29
We extend the results on the uniform convergence of Bieberbach polynomials to domains with certain interior zero angles (outward pointing cusps), and show that they play a special role in the problem....
Askey-Wilson polynomials: an affine Hecke algebraic approach
Askey-Wilson polynomials affine Hecke algebraic approach
2010/10/29
We study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogonality relations for non-symmetric and anti-symmetric Askey-Wi...