Related papers: Frames by Multiplication
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In…
Let $M$ be a complete non-compact Riemannian manifold satisfying the doubling volume property as well as a Gaussian upper bound for the corresponding heat kernel. We study the boundedness of the Riesz transform $d\Delta ^{-\frac{1}{2}}$ on…
We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
Simultaneous tiling for several different translational sets has been studied rather extensively, particularly in connection with the Steinhaus problem. The study of orthonormal wavelets in recent years, particularly for arbitrary dilation…
A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…
By applying new functional analysis tools in the framework of Fourier interpolation formulas, such as sc-Fredholm operators and Schauder frames, we are able to improve and refine several properties of these aforementioned formulas on the…
We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an $\epsilon>0$ such that, conditioned on a folklore conjecture in…
We extend Robertson's theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone's theorem and the theory of spectral multiplicity to analyze wandering frame…
In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will…
The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…
Motivated by the dynamical sampling problem, we study frames in an infinite dimensional Hilbert space generated by the iterates of a bounded operator T, also known as dynamical frames. We first characterize the operators that generate…
Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In a general setting they can be described as frame multipliers, consisting of analysis, multiplication by…
We analyze spectra and the Riesz property of spectral projections of non-symmetric perturbations of self-adjoint operators with eigenvalues having arbitrary multiplicities, including infinite ones. In particular, we establish the Riesz…
When extending the Ehrhart lattice point enumerator $L_P(t)$ to allow real dilation parameters $t$, we lose the invariance under integer translations that exists when $t$ is restricted to be an integer. This paper studies this phenomenon;…
Given an orthonormal basis $ {\mathcal V}= \{v_j\} _{j\in N}$ in a separable Hilbert space $H$ and a set of unit vectors $ {\mathcal B}=\{w_j\}_{j\in N}$, we consider the sets $ {\mathcal B}_N$ obtained by replacing the vectors $v_1, ...,\,…
We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…
We construct a family of spline affine Riesz bases, i.e. sequences of dilations and translations generated by the special spline functions $\psi_m$, and we prove that their Riesz bounds are independent of $m$. We put $\psi_0=\chi$ as the…
Let $S\subset\R^d$ be a bounded subset with positive Lebesgue measure. The Paley-Wiener space associated to $S$, $PW_S$, is defined to be the set of all square-integrable functions on $\R^d$ whose Fourier transforms vanish outside $S$. A…
We apply Lax-Milgram theorem to characterize scalable and piecewise scalable frame in finite and infinite-dimensional Hilbert spaces. We also introduce a method for approximating the inverse frame operator using finite-dimensional linear…