相关论文: Riesz Bounds of Spline Affine Systems

Inspired by the work of Hedenmalm, Lindqvist and Seip, we consider different properties of dilations systems of a fixed function $\varphi \in L^2(0,1)$. More precisely, we study when the system $\{\varphi(nx)\}_n$ is a Bessel sequence, a…

Given a function $\psi$ in $ \LL^2(\R^d)$, the affine (wavelet) system generated by $\psi$, associated to an invertible matrix $a$ and a lattice $\zG$, is the collection of functions $\{|\det a|^{j/2} \psi(a^jx-\gamma): j \in \Z, \gamma \in…

The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a 1D spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact…

A bounded, Riemann integrable and measurable set $K\subset \mathbb{R}^d$, which fulfills \[\sum\limits_{\gamma\in\Gamma}\mathbb{1}_K(x-\gamma)=k\text{ almost everywhere, $x\in\mathbb{R}^d$}\] for a lattice $\Gamma\subset\mathbb{R}^d$ is…

We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of…

In this paper, we consider the nonselfadjoint Sturm Liouville operator with and either periodic, or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a…

In this paper we formulate a concrete method for determining whether a system of dilated periodic functions forms a Riesz basis in $L^2(0,1)$. This method relies on a general framework developed by Hedenmalm, Lindqvist and Seip about 20…

Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…

We characterize orthonormal bases, Riesz bases and frames which arise from the action of a countable discrete group $\Gamma$ on a single element $\psi$ of a given Hilbert space $\mathcal{H}$. As $\Gamma$ might not be abelian, this is done…

In this work, we prove that certain L^2-unbounded transformations of orthogonal wavelet bases generate vaguelets. The L^2-unbounded functions involved in the transformations are assumed to be quasi-homogeneous at high frequencies. We…

A particular consequence of the famous Carleson-Hunt theorem is that the Taylor series expansions of bounded holomorphic functions on the open unit disk converge almost everywhere on the boundary, whereas on single points the convergence…

Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbb Z)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$ is strictly increasing, and the set of functions $\{\mathbb R\ni t\mapsto e^{ix_jt}:j\in\mathbb Z\}$ is a…

We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that ifthetranslates are taken only from a subset of the natural…

We introduce a framework for spline spaces of hierarchical type, based on a parent-children relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. Such framework makes it simple…

In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited…

Based on two point spline approximations of arbitrary order, a series of functions that define lower bounds for sin(x) and sin(x)/x, over the interval [0,Pi/2], with increasingly low relative errors and smaller relative errors than…

Border basis schemes are open subschemes of the Hilbert scheme of $\mu$ points in an affine space $\mathbb{A}^n$. They have easily describable systems of generators of their vanishing ideals for a natural embedding into a large affine space…

The notions of Bessel sequence, Riesz-Fischer sequence and Riesz basis are generalized to a rigged Hilbert space $\D[t] \subset \H \subset \D^\times[t^\times]$. A Riesz-like basis, in particular, is obtained by considering a sequence…

For p-subordinate perturbations of unbounded normal operators, the change of the spectrum is studied and spectral criteria for the existence of a Riesz basis with parentheses of root vectors are established. A Riesz basis without…

We show that any finite union of intervals supports a Riesz basis of exponentials