Related papers: Approximation of the Lagrange and Markov spectra
We examine the utility of the quadratic pseudospectrum in photonics and condensed matter. Specifically, the quadratic pseudospectrum represents a method for approaching systems with incompatible observables, as it both minimizes the…
In this paper, we give a definition of Diophantine points of type $\gamma$ for $\gamma\geq0$ in a homogeneous space $G/\Gamma$, and compute the Hausdorff dimension of the subset of points which are not Diophantine of type $\gamma$ when $G$…
In this paper, we consider two dynamical systems associated to the nearest integer continued fraction, and show that both of them have full Hausdorff dimension spectrum.
We demonstrate criteria, purely based on finite subwords of the potential, to guarantee spectral inclusion as well as Hausdorff approximation of pseudospectra or even spectra of generalized Schr\"odinger operators on the discrete line or…
The transfer matrix method is applied to quasi one-dimensional and one-dimensional disordered systems with long-range interactions, described by band random matrices. We investigate the convergence properties of the whole Lyapunov spectra…
We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are…
We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum…
This paper concerns extension of the classical Lagrange theorem, on the eventual periodicity of continued fraction expansions of quadratic surds, and the versions of it found in the literature in the case of complex numbers. In this…
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…
We consider numerical approximations of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consist of a sinc quadrature coupled with…
We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the…
In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine-Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on…
The discrete part of the Markoff spectrum on the Hecke group of index 6 was determined by A.~Schmidt. In this paper, we study its Markoff and Lagrange spectra after the smallest accumulation point $4/\sqrt3$. We show that both the Markoff…
We prove that for any $\eta$ that belongs to the closure of the interior of the Markov and Lagrange spectra, the sets $k^{-1}((-\infty,\eta])$ and $k^{-1}(\eta)$, which are the sets of irrational numbers with best constant of Diophantine…
We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically…
We investigate approximation to a given real number by algebraic numbers and algebraic integers of prescribed degree. We deal with both best and uniform approximation, and highlight the similarities and differences compared with the…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
The Hausdorff dimension of an exceptional set of periods for which convergence of a formal solution to an inhomogeneous wave equation in n spatial and one temporal dimension is problematic, is determined along with conditions which the…
The paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization problem is tackled using a multi-dimensional…
This paper proposes a hierarchical spatial-temporal model for modelling the spectrograms of animal calls. The motivation stems from analyzing recordings of the so-called grunt calls emitted by various lemur species. Our goal is to identify…