Related papers: Some computable Wiener-Hopf determinants and polyn…
We consider the image of the operator inducing the determinantal point process with the confluent hypergeometric kernel. The space is described as the image of $L_2[0, 1]$ under a unitary transform, which generalizes the Fourier transform.…
We prove Wigner-Eckart theorem for the irreducible tensor operators for arbitrary Hopf algebras, provided that tensor product of their irreducible representation is completely reducible. The proof is based on the properties of the…
The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds,…
For the Hahn and Krawtchouk polynomials orthogonal on the set $\{0, \ldots,N\}$ new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These…
We review the asymptotic behavior of a class of Toeplitz (as well as related Hankel and Toeplitz + Hankel) determinants which arise in integrable models and other contexts. We discuss Szego, Fisher-Hartwig asymptotics, and how a transition…
We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for…
In this note, we present a systematic method to explicitly compute the determinants and inverses for some generalized Hilbert matrices associated with orthogonal systems with explicit representations. We expressed the determinant, the…
We calculate the Hankel determinants of sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries' natural and deep connection with…
We derive identities for the determinants of matrices whose entries are (rising) powers of (products of) polynomials that satisfy a recurrence relation. In particular, these results cover the cases for Fibonacci polynomials, Lucas…
We compute the full off-diagonal asymptotics of the equivariant and partial Bergman kernels associated with a circle action on a prequantized K\"ahler manifold with bounded geometry at infinity, then use these results to compute the…
In case of the KP hierarchy where the dependent variable takes values in an (arbitrary) associative algebra A, it is known that there are solutions which can be expressed in terms of quasideterminants of a Wronski matrix which solves the…
In this paper we determine the asymptotics of the determinant of Bessel operators for sufficiently smooth generating functions. These operators are similar to Wiener-Hopf operators with the Fourier transform replaced by the Hankel transform…
Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…
The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed…
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This…
We provide a representation in terms of certain canonical functions for a sequence of polynomials orthogonal with respect to a weight that is strictly positive and analytic on the unit circle. These formulas yield a complete asymptotic…
The Varchenko determinant is the determinant of the bilinear form associated to a real hyperplane arrangement. We show that we can obtain the exact value of this determinant for certain hyperplane arrangements if we know the edges which are…
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for…
We give four examples of families of orthogonal polynomials for which the coefficients in the recurrence relation satisfy a discrete Painlev\'e equation. The first example deals with Freud weights $|x|^\rho \exp(-|x|^m)$ on the real line,…
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…