Related papers: Transformations preserving the effective spectral …
The competitive spectral radius extends the notion of joint spectral radius to the two-player case: two players alternatively select matrices in prescribed compact sets, resulting in an infinite matrix product; one player wishes to maximize…
Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators
In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
I investigate the scattering properties of transformation devices as the traditional impedance matching criteria are altered. This is demonstrated using simple theory and augmented by numerical simulations that investigate the role of…
We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…
In this paper we investigate the spectral norm for circulant matrices, whose entries are modified Fibonacci numbers and Lucas numbers. We obtain the identity estimations for the spectral norms. Some numerical test results are listed to…
We extend the T-matrix approach to light scattering by spherical particles to some simple cases in which the scatterers are optically anisotropic. Specifically we consider cases in which the spherical particles include radially and…
We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of…
The spectrum of a real and symmetric $N\times N$ matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. In the first part of this work we…
We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues…
By solving Maxwell equations with the ideal-metal boundary conditions in the TM case, we have fully described the transmission and diffraction properties of a single slit regardless of its width. Efficiencies of the main transformation…
The Lorentz transformations for the optical constants (electric permittivity, magnetic permeability and index of refraction) of moving media are considered.
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.
A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…