Related papers: The Third Hankel determinant for inverse coefficie…
We study the integral torsion of the values of strict polynomial functors defined over the integers. We interpret some classical homological invariants as values of strict polynomial functors and therefore obtain estimates of the integral…
More analysis of operator determinants on homogeneous three dimensional lens spaces is presented with the emphasis on numerics so that Laplacians for massive fields can be dealt with. Polyhedral quotients are also briefly considered.…
We view the determinant and permanent as functions on directed weighted graphs and introduce their analogues for the undirected graphs. We prove that the task of computing the undirected determinants as well as permanents for planar graphs,…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
We prove and generalize a conjecture of Johann Cigler on the Hankel determinants of convolution powers of Narayana polynomials. Our method follows a "guess-and-prove" strategy, relying on established techniques involving Hankel continued…
We describe the structure of the resolvent of the discrete rough truncated Hilbert transform under the critical exponent. This extends the results obtained in [8].
We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of Jack polynomials.
We introduce the notion of Dunkl positive definite and strictly positive definite functions on $\mathbb{R}^{d}$. This done by the use of the properties of Dunkl translation. We establish the analogue of Bochner's theorem in Dunkl setting.…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
In this note, we show that the space associated with sub-Hankel determinant is a non-reductive, regular prehomogeneous vector space, and we give the multiplicative Legendre transforms of sub-Hankel determinants. Moreover we observe certain…
We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…
The fractional Calder\'on problem asks to determine the unknown coefficients in a nonlocal, elliptic equation of fractional order from exterior measurements of its solutions. There has been substantial work on many aspects of this inverse…
The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…
Given a block triangular matrix $M$ over a noncommutative ring with invertible diagonal blocks, this work gives two new representations of its inverse $M^{-1}$. Each block element of $M^{-1}$ is explicitly expressed via a quasideterminant…
The direct and inverse problems for a third-order self-adjoint differential operator with non-local potential functions are considered. Firstly, the multiplicity for eigenvalues of the operator is analyzed, and it is proved that the…
We consider a Hankel determinant formula for generic solutions of the Painlev\'e IV equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
We consider the following perturbed polyharmonic operator $\Lc(x,D)$ of order $2m$ defined in a bounded domain $\Omega \subset \mathbb{R}^n, n\geq 3$ with smooth boundary, as \begin{equation*} \Lc(x,D) \equiv (-\Delta)^m +…
The symmetrized Slater determinants of orthogonal polynomials with respect to a non-negative Borel measure are shown to be represented by constant multiple of Hankel determinants of two other families of polynomials, and they can also be…
We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.