Related papers: K-Spectral Sets
The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these…
We prove a lower bound on the first eigenvalue of the fractional Dirichlet-Laplacian of order $s$ on planar open sets, in terms of their inradius and topology. The result is optimal, in many respects. In particular, we recover a classical…
For random matrix models, the parameter estimation based on the traditional likelihood functions is not straightforward in particular when we have only one sample matrix. We introduce a new parameter optimization method for random matrix…
This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations…
In distributed optimization or Nash-equilibrium seeking over directed graphs, it is crucial to find a matrix norm under which the disagreement of individual agents' states contracts. In existing results, the matrix norm is usually defined…
We study the spectral properties of infinitely smooth multivariate kernel matrices when the nodes form a single cluster. We show that the geometry of the nodes plays an important role in the scaling of the eigenvalues of these kernel…
In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we introduce shrinkable hemirings and prove that dense division…
The K-matrix, also known as the "Wigner reaction matrix" in nuclear scattering or "impedance matrix" in the electromagnetic wave scattering, is given essentially by an M x M diagonal block of the resolvent (E-H)^{-1} of a Hamiltonian H. For…
The local spectrum of a vertex set in a graph has been proven to be very useful to study some of its metric properties. It also has applications in the area of pseudo-distance-regularity around a set and can be used to obtain quasi-spectral…
We present a new formula for the Cauchy index of a rational function on an interval using subresultant polynomials. There is no condition on the endpoints of the interval and the formula also involves in some cases less subresultant…
We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the "population spectrum"), given access to samples drawn from the…
Recently Burkhardt et. al. introduced the $k$-checkerboard random matrix ensembles, which have a split limiting behavior of the eigenvalues (in the limit all but $k$ of the eigenvalues are on the order of $\sqrt{N}$ and converge to…
A method is introduced to derive resolution criteria for various a priori defined templates of brightness distribution fitted to represent structures and objects in astronomical images. The method is used for deriving criteria for the…
It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random NxN Hermitian matrices. Our main goal is to…
The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
Understanding the evolution of the Milky Way calls for the precise abundance determination of many elements in many stars. A common perception is that deriving more than a few elemental abundances ([Fe/H], [$\alpha$/Fe], perhaps [C/H],…
The paper addresses the problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under two standard kinds of assumptions --…
In this paper a new explicit integral formula is derived for solutions of the tangential Cauchy-Riemann equations on CR q-concave manifolds and optimal estimates in the Lipschitz norms are obtained.
This paper deals with spectral inequalities for one-dimensional Schr\"odinger operators with potentials bounded between two increasing functions (weights). The spectral inequality allows one to estimate the norm of a function with bounded…