Related papers: Exponential frames for unbounded sets

Given $\lambda\in(0, 1)$, let $E_\lambda$ be the self-similar set generated by the iterated function system $\{x/3,(x+\lambda)/3,(x+2)/3\}$. Then $E_\lambda$ is a self-similar set with overlaps. We obtain the necessary and sufficient…

Let $M$ be a $d$-dimensional closed Riemannian manifold, let $f\in\mathrm{Diff}^{1+\beta}(M)$, and denote by $m$ the Riemannian volume form of $M$. We prove that if $m\circ f^{-n}\xrightarrow[n\to\infty]{}\mu$ exponentially fast, then $\mu$…

This paper presents new results concerning the observer design for wide classes of nonlinear systems with both sampled and delayed measurements. By using a small gain approach we provide sufficient conditions, which involve both the delay…

This paper demonstrates the existence of a finite set of equilibria in the case of the indeterminacy of linear rational expectations models. The number of equilibria corresponds to the number of ways to select n eigenvectors among a larger…

Let $\Lambda$ be the limit set of an infinite conformal iterated function system and let $F$ denote the set of fixed points of the maps. We prove that the box dimension of $\Lambda$ exists if and only if \[ \overline{\dim}_{\mathrm B} F\leq…

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…

In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight frame. In this paper we define…

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to…

We discuss existence and stability of Riesz bases of exponential type of L^2(T) for special domains T called trapezoids. We construct exponential bases on L^2(T) when T is a finite union of rectangles with the same height. We also…

The paper studies finite extensions of Bessel sequences in infinite-dimensional Hilbert spaces. We provide a characterization of Bessel sequences that can be extended to frames by adding finitely many vectors. We also characterize frames…

We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the…

$L$-ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant $L$-ensembles are the subclass which are locally translationally invariant and…

Let $A\colon H\rightarrow H$ be a normal operator on an infinite-dimensional separable Hilbert space $H$ and let $S\subseteq H$ be a finite subset such that $\{A^nx\}_{n\geq 0,\,x\in S}$ can be rescaled to form a frame for $H$. That is,…

The inferential model (IM) framework produces data-dependent, non-additive degrees of belief about the unknown parameter that are provably valid. The validity property guarantees, among other things, that inference procedures derived from…

We consider a family of measures $\mu$ supported in $\br^d$ and generated in the sense of Hutchinson by a finite family of affine transformations. It is known that interesting sub-families of these measures allow for an orthogonal basis in…

We consider sampling strategies for a class of multivariate bandlimited functions $f$ that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating $f$ to the…

How can we perform a metrological task if only limited control over a quantum system is given? Here, we present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. Our approach…