Related papers: Examples of exponential bases on Union of interval…
We construct explicit exponential bases on finite unions of disjoint rectangles of $\mathbb{R}^d$ with rational vertices.
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 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.
We construct explicit exponential bases on triangles in R^2 and on infinite unions of segments on the real line.
We show that any finite union of intervals supports a Riesz basis of exponentials
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…
We extend the classical Kadec 1/4 theorem for systems of exponential functions on an interval to frames and atomic decompositions formed by sampling an orbit of a vector under an isometric group representation.
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 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…
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…
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 study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…
We prove that every finite union of rectangles in $R^d$ admits a Riesz basis of exponentials.
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…
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…
It is shown that if a $d$-dimensional cube is decomposed into n cubes, the side lengths of which belong to the interval $\left(1-\frac{1}{n^{1/d}+1}, 1\right], then $n$ is a perfect $d$-th power and all cubes are of the same size. This…
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 prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous…
In this paper we consider the iteration of infinitely many signed exponentials with the same base but the signs may vary. We show that for every base in an explicit interval this iteration converges for any sequence of signs and all the…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…