Related papers: On associative spectra of operations
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately…
Following the pioneering work of Duistermaat and Gr\"unbaum, we call a family $\{p_n(x)\}_{n=0}^{\infty}$ of polynomials bispectral, if the polynomials are simultaneously eigenfunctions of two commutative algebras of operators: one…
We consider the complex solvable non-commutative two dimensional Lie algebra $L$, $L=<y>\oplus <x>$, with Lie bracket $[x,y]=y$, as linear bounded operators acting on a complex Hilbert space $H$. Under the assumption $R(y)$ closed, we…
We introduce a novel approach to measure the behavior of a geometric operator before and after coarsening. By comparing eigenvectors of the input operator and its coarsened counterpart, we can quantitatively and visually analyze how well…
We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…
Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…
The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative algebra.
The $J$-matrix method is extended to difference and $q$-difference operators and is applied to several explicit differential, difference, $q$-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
A matrix pattern is often either a sign pattern with entries in {0,+,-} or, more simply, a nonzero pattern with entries in {0,*}. A matrix pattern A is spectrally arbitrary if for any choice of a real matrix spectrum, there is a real matrix…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are…
Actions of a locally compact group G on a measure space X give rise to unitary representations of G on Hilbert spaces. We review results on the rigidity of these actions from the spectral point of view, that is, results about the existence…
We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…
The paper gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from $x$ to $y$ is equal to the complex unity…
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rough classification of large empirical graphs into families…
This paper develops the theory behind the bispectrum, a concept that is well established in statistical signal processing but not, until recently, extended to computer vision as a source of frequency-domain invariants. Recent papers on…