相关论文: On Fourier frames

We prove that if every element $u$ in a Hilbert space $H$ admits a representation as unconditionally convergent series $$u=\sum_{k=1}^\infty \langle u, y_k\rangle x_k,$$ then there exist nonzero scalars $\{\alpha_k\}_{k=1}^\infty$ such that…

We consider bounded operators $A$ acting iteratively on a finite set of vectors $\{f_i : i\in I\}$ in a Hilbert space $\mathcal H$ and address the problem of providing necessary and sufficient conditions for the collection of iterates…

The product of any number of Legendre functions, under a restricted domain, can be expanded by the corresponding Legendre polynomials, with the coefficient being the sinc function. While an analogous expansion can be made for any number of…

An analogue of the KP hierarchy, the SDiff(2) KP hierarchy, related to the group of area-preserving diffeomorphisms on a cylinder is proposed. An improved Lax formalism of the KP hierarchy is shown to give a prototype of this new hierarchy.…

In this paper, we analyze a function space consisting of functions for which both the function and its Fourier transform exhibit Gaussian decay together with exponential growth governed by suitable weight functions. First, we examine…

In this paper we begin the study of Schur analysis and de Branges-Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like…

In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\boldsymbol k)$,…

We consider the Fock space weighted by $e^{-\alpha |z|^{2}}$, of entire and quasi-periodic (modulo a weight dependent on $\nu $) functions on ${C}$. The quotient space $\mathbb{C}/\mathbb{Z}$, called `The flat cylinder', is represented by…

In this paper we solve the problem of approximating functionals $(\varphi(A)x, f)$ (where $\varphi(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another…

We prove that if $f(n)$ is a Steinhaus or Rademacher random multiplicative function, there almost surely exist arbitrarily large values of $x$ for which $|\sum_{n \leq x} f(n)| \geq \sqrt{x} (\log\log x)^{1/4+o(1)}$. This is the first such…

We study approximate solutions of the Wheeler DeWitt (WdW) equation and compare them with the standard results of cosmological perturbation theory. In mini-superspace, we introduce a dimensionless gravitational coupling $\alpha$ that is…

About forty years ago it was realized by several researchers that the essential features of certain objects of Probability theory, notably Gaussian processes and limit theorems, may be better understood if they are considered in settings…

We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…

Large-scale graph machine learning is challenging as the complexity of learning models scales with the graph size. Subsampling the graph is a viable alternative, but sampling on graphs is nontrivial as graphs are non-Euclidean. Existing…

We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…

Given a set $S$ of small measure, we discuss existence of sampling sequences for the Paley-Wiener space $PW_S$, which have both densities and sampling bounds close to the optimal ones.

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form $\{T^i f_1\}_{i\in \mathbb{N}}$, where $f_1$ belongs to Hilbert space $\h$ and $T:\h\rightarrow\h$ belongs to certain classes of the…

For estimating a positive normal mean, Zhang and Woodroofe (2003) as well as Roe and Woodroofe (2000) investigate 100($1-\alpha)%$ HPD credible sets associated with priors obtained as the truncation of noninformative priors onto the…

The following problem is studied in this paper: Which multipliers $\{\lambda_{k, n}\}$ ensure the convergence, as $n\to \infty$, of the linear means of the Fourier series of functions $f\in L_1[-\pi, \pi]$ $$ \sum_{k=-\infty}^\infty…

We open a new perspective on the sup-norm problem and propose a version for non-spherical Maass forms when the maximal compact K is non-abelian and the dimension of the K-type gets large. We solve this problem for an arithmetic quotient of…