相关论文: On Asymptotics of Polynomial Eigenfunctions for Ex…

It is proposed the algorithm that find a basis of the ideal and a basis of the space of all root functionals by using the extension operation for bounded root functionals, when the number of polynomials is equal to the number of variables,…

We propose a way to find the asymptotic distribution of zeros of orthogonal polynomials p_n(x) satisfying a difference equation of the form B(x)p_n(x+\delta)-C(x,n)p_n(x)+D(x)p_n(x-\delta)=0. We calculate the asymptotic distribution of…

We consider an inverse problem for Schr\"odinger operators on connected equilateral graphs with standard matching conditions. We calculate the spectral determinant and prove that the asymptotic distribution of a subset of its zeros can be…

We find uniform asymptotic formulas for all the eigenvalues of certain 7-diagonal symmetric Toeplitz matrices of large dimension. The entries of the matrices are real and we consider the case where the real-valued generating function such…

For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit disctibution in the complex plane as the…

We introduce a new representation for the rescaled Appell polynomials and use it to obtain asymptotic expansions to arbitrary order. This representation consists of a finite sum and an integral over a universal contour (i.e. independent of…

In this paper, we study the random polynomial $p_n(\rho):=\prod_{j=1}^n (|z_j|-\rho)$, where the points $\{z_j\}_{j=1}^n$ are the eigenvalue moduli of random normal matrices with a radially symmetric potential. We establish precise large…

We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we found an interesting identity which is used to describe the spectral…

We use directed graphs called "syzygy quivers" to study the asymptotic growth rates of the dimensions of the syzygies of representations of finite dimensional algebras. For any finitely generated representation of a monomial algebra, we…

We study continuity of the roots of nonmonic polynomials as a function of their coefficients using only the most elementary results from an introductory course in real analysis and the theory of single variable polynomials. Our approach…

Asymptotic behavior of orthogonal polynomials on the circle, with respect to a weight having a fractional zero on the torus. Applications to the eigenvalues of certain unitary random matrices. This paper is devoted to the orthogonal…

We construct and classify all polynomial growth solutions to certain drift-harmonic equations on complete manifolds with paraboloidal asymptotics. These encompass the natural drift-harmonic equations on certain steady gradient Ricci…

We introduce a theorem currently proved unique by the asymptotic behaviors of eigenvalues of a compact operator. Specifically, a problem of partitions is considered and the Neumann--Poincar\'e operator is employed as the compact linear…

In this paper are discussed the results of new numerical experiments on zero distribution of type I Hermite-Pad\'e polynomials of order $n=200$ for three different collections of three functions $[1,f_1,f_2]$. These results are obtained by…

We consider non-self-adjoint electromagnetic Schr\"odinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic…

We further investigate the relations between the large degree asymptotics of the number of real zeros of random trigonometric polynomials with dependent coefficients and the underlying correlation function. We consider trigonometric…

In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the signs of the parameters, we classify the difference…

In this paper, we enlarge the space of uniformly supported pseudo-differential operators on some groupoids by considering kernels satisfying certain asymptotic estimates. We show that such enlarged space contains the compact parametrix, and…

We obtain Plancherel-Rotach type asymptotics valid in all regions of the complex plane for orthogonal polynomials with varying weights of the form $e^{-NV(x)}$ on the real line, assuming that $V$ has only two Lipschitz continuous…

In this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions $g$ and $h$, where $g$ is normalized, of moderate growth, and $0<h(n) \leq h(n+1)$. We put $P_0^{g,h}(x)=1$ and…