相关论文: Unions of exponential Riesz bases

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…

Let $S$ be the union of finitely many disjoint intervals on the real line. Suppose that there are two real numbers $\alpha, \beta$ such that the length of each interval belongs to $Z \alpha + Z \beta$. We use quasicrystals to construct a…

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

We give sufficient conditions for the exponential system to be a Riesz basis in $L^2(E)$, where $E$ is a union of two intervals. We show that these conditions are close to be necessary. In addition, we demonstrate ``extra point effect'' for…

We construct explicit exponential bases on triangles in R^2 and on infinite unions of segments on the real line.

We construct explicit exponential bases on finite unions of disjoint rectangles of $\mathbb{R}^d$ with rational vertices.

In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…

The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted…

We find explicit stability bounds for exponential Riesz bases on domains of R^d. Our results generalize Kadec theorem and other stability theorems in the literature.

In this paper, we construct explicit exponential bases on finite or infinite unions of segments of total length one with some conditions on gaps between them. We also construct exponential bases on certain unions of cubes in $\R^d$ and we…

We prove that every finite union of rectangles in $R^d$ admits a Riesz basis of exponentials.

Let $G$ be a closed subgroup of ${\mathbb R}^d$ and let $\nu$ be a Borel probability measure admitting a Riesz basis of exponentials with frequency sets in the dual group $G^{\perp}$. We form a multi-tiling measure $\mu = \mu_1+...+\mu_N$…

For a partition of $[0,1]$ into intervals $I_1,\ldots,I_n$ we prove the existence of a partition of $\mathbb{Z}$ into $\Lambda_1,\ldots, \Lambda_n$ such that the complex exponential functions with frequencies in $ \Lambda_k$ form a Riesz…

We characterize exponential systems on sets of finite measure that form a frame or a Riesz sequence at the critical density. Namely, they are precisely those systems for which the underlying point set admits a weak limit that yields a Riesz…

We consider systems of exponentials with frequencies belonging to simple quasicrystals in $\mathbb{R}^d$. We ask if there exist domains $S$ in $\mathbb{R}^d$ which admit such a system as a Riesz basis for the space $L^2(S)$. We prove that…

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 extend to several dimensions the result of K. Seip and Y.I. Lyubarskii that proves the existence of Riesz basis of exponentials for a finite union of intervals with equals lengths.

We consider \textit{additive spaces}, consisting of two intervals of unit length or two general probability measures on ${\mathbb R}^1$, positioned on the axes in ${\mathbb R}^2$, with a natural additive measure $\rho$. We study the…

Linear combinations of exponentials $e^{i\lambda_kt}$ in the case where the distance between some points $\lambda_k$ tends to zero are studied. D. Ullrich has proved the basis property of the divided differences of exponentials in the case…

We consider three special and significant cases of the following problem. Let D be a (possibly unbounded) set of finite Lebesgue measure in R^d. Find conditions on D for which the standard exponential basis on the unit cube of R^d is a…