Related papers: Sampling in paley-wiener spaces on combinatorial g…

A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of…

We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…

In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…

Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…

We consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley-Wiener space. These…

This paper introduces a notion of presentation for locally inverse semigroups and develops a graph structure to describe the elements of locally inverse semigroups given by these presentations. These graphs will have a role similar to the…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…

In this paper we study polynomial maps of vector spaces and their eigenvectors and eigenvalues. The new quantity called complanart is defined. Complanarts determine complanarity of solution vectors of systems of polynomial equations.…

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…

We study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz-Zygmund inequalities in subspaces of polynomials. We focus on the study of the Hardy space and the Bergman…

We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…

A new method for constructing self-referential tilings of Euclidean space from a graph directed iterated function system, based on a combinatorial structure we call a pre-tree, is introduced. In the special case that we refer to as…

Previous results on certain sampling series have left open if divergence only occurs for certain subsequences or, in fact, in the limit. Here we prove that divergence occurs in the limit. We consider three canonical reconstruction methods…

Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary,…

Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…

Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and…

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…

We prove an analogue of the pointwise Weyl law for families of unitary matrices obtained from quantization of one-dimensional interval maps. This quantization for interval maps was introduced by Pako\'nski et al. [J. Phys. A: Math. Gen. 34…

We investigate the connection between translation bases for Paley-Wiener spaces and exponential Fourier bases for a domain. We apply these results to the characterization of vector-valued time-frequency translates of a Paley-Wiener "window"…

The de Branges spaces of entire functions generalise the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of…