Related papers: Spectral sets for numerical range
We briefly describe some well-known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic mean, motivate the definition of a new kind of mean that we…
We identify points of difference between Invariant Set Theory and standard quantum theory, and show that these lead to noticeable differences in predictions between the two theories. We design a number of experiments to test which of these…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
The attracting set and the inverse limit set are important objects associated to a self-map on a set. We call \emph{stable set} of the self-map the projection of the inverse limit set. It is included in the attracting set, but is not equal…
Let X be a definable sub-set of some o-minimal structure. We study the spectrum of X, in relation with the definability of types.
In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to…
The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger…
Fractals with different levels of self-similarity and magnification are defined as reduced fractals. It is shown that spectra of these reduced fractals can be constructed and used to describe levels of complexity of natural phenomena.…
There has been quite some activity and progress concerning spectral asymptotics of random operators that are defined on percolation subgraphs of different types of graphs. In this short survey we record some of these results and explain the…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
The spectral gap is estimated for measure-valued diffusion processes induced by the intrinsic/extrinsic derivatives on the space of finite measures over a Riemannian manifold. This provides explicit exponential convergence rate for these…
We introduce a new tool to study the spectral type of rank one transformations using the method of central limit theorem for trigonometric sums. We get some new applications.
The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in…
We present an overview of concepts and results obtained with statistical models in study of nuclear multifragmentation. Conceptual differences between statistical and dynamical approaches, and selection of experimental observables for…