相关论文: A quantitative Balian-Low theorem for higher dimen…

We formulate and prove finite dimensional analogs for the classical Balian-Low theorem, and for a quantitative Balian-Low type theorem that, in the case of the real line, we obtained in a previous work. Moreover, we show that these results…

Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on $\mathbb{Z}_d$. Here we extend these results to a multivariable setting. Additionally, we show a variety of applications of the…

We study functions generating Gabor Riesz bases on the integer lattice. The classical Balian-Low theorem restricts the simultaneous time and frequency localization of such functions. We obtain a quantitative estimate that extends both this…

In this paper we extend the Balian--Low theorem, which is a version of the uncertainty principle for Gabor (Weyl--Heisenberg) systems, to functions of several variables. In particular, we first prove the Balian--Low theorem for arbitrary…

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor-Riesz bases and a constant curvature connection on projective modules over noncommutative tori.

We prove a quantitative Borg-Levinson theorem for a large class of unbounded potentials. We give a detailed proof when the dimension of the space is greater than or equal to five. We also indicate the modifications necessary to cover lower…

We establish cohomological and extension dimension versions of the Hurewicz dimension-raising theorem

The Gross-Kohnen-Zagier theorem describes Heegner points on a modular curve in terms of coefficients of modular forms. We give another proof of this theorem which generalizes to higher dimensions.

We give simple upper and lower bounds for the order of a Klein geometry

An extension of the Wigner-Araki-Yanase theorem to multiplicative conserved quantities is presented and approximate versions of the theorem are discussed.

We prove finite-field analogs of Bourgain's projection theorem in higher dimensions. In particular, for a certain range of parameters we improve on an exceptional set estimate by Chen in all dimensions and codimensions.

In this paper we will give the calculus, the criterion, and the existence of the arithmetic Galois covers of higher relative dimensions.

We modify the quantization of Etingof and Kazhdan so that it can be used to quantize quasi-Lie bialgebras.

We extend the Balian-Low theorem to Gabor subspaces of $L^2(\mathbb R)$ by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating…

In this paper, the equidistribution theorem of Szpiro-Ullmo-Zhang about sequences of small points in an abelian variety is extended to the case of sequences of higher dimensional subvarieties. A quantitative version of this result is also…

We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued…

We consider the extension of the Jackson calculus into higher dimensions and specifically into Clifford analysis.

In this paper, we review the recently formulated quantum laws of motion and provide new observations. We also extend these laws to higher dimensions. By applying in two dimensions the obtained relations to charge submitted to an electric…

We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are…