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Matrix elements of irreducible representations of SU(n + 1)×SU(n + 1) and multivariable matrix-valued orthogonal polynomials
(Academic Press Inc Elsevier Science, 2020-04-15)
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking ...
The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
(Wiley VCH Verlag, 2020-12-11)
Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous polynomial P(z)=∑|α|=maαzα in n complex variables, (∑|α|=m|aα|r)1/r≤Amp,r(n)supz∈Bℓnp∣∣P(z)∣∣. For every degree m, and a ...
Orthant probabilities and the attainment of maxima on a vertex of a simplex
(Elsevier, 2021-02)
We calculate bounds for orthant probabilities for the equicorrelated multivariate normal distribution and use these bounds to show the following: for degree k>4, the probability that a k-homogeneous polynomial in n variables ...
Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces
(Springer, 2012-02)
For a real square-free multivariate polynomial F, we treat the general problem of finding real solutions of the equation F=0, provided that the real solution set {F=0}ℝ is compact. We allow that the equation F=0 may have ...
JH-singularity and JH-regularity of multivariate stationary processes over LCA groups
(Kazimierz Urbanik Center for Probability and Mathematical Statistics, 2021-04)
Let G be an LCA group, I' its dual group, and H a closed subgroup of G such that its annihilator is countable. Let M denote a regular positive semidefinite matrix-valued Borel measure on I' and L^2(M) the corresponding ...
Closed formula for univariate subresultants in multiple roots
(Elsevier Science Inc, 2019-03)
We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials as a function of their roots independently of their multiplicity structure. This is the first ...