m at h . C A ] 9 O ct 2 01 7 FRAMES OF EXPONENTIALS AND SUB – MULTITILES IN LCA GROUPS
نویسنده
چکیده
In this note we investigate the existence of frames of exponentials for L(Ω) in the setting of LCA groups. Our main result shows that sub–multitiling properties of Ω ⊂ Ĝ with respect to a uniform lattice Γ of Ĝ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames.
منابع مشابه
O ct 2 01 0 PROPERTIES OF UNIFORM DOUBLY STOCHASTIC MATRICES
We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential distributions and indeed even large sub-matrices of side-length o(n) behave like independent exponentials. We determine the limiting empirical distribution of the si...
متن کاملOn TC0 Lower Bounds for the Permanent
In this paper we consider the problem of proving lower bounds for the permanent. An ongoing line of research has shown super-polynomial lower bounds for slightly-non-uniform small-depth threshold and arithmetic circuits [All99, KP09, JS11, JS12]. We prove a new parameterized lower bound that includes each of the previous results as sub-cases. Our main result implies that the permanent does not ...
متن کاملSome Remarks on Reflection Positivity*)
120 Czech. J. Phys. B 29 [1979] A. Uhlmann: Some remarks on reflection positivity There was given, (c), a subspace L+ of L with RP property (~ ,0~) > 0 fora l l ~ L + . Then there appeared, (d), an isometric 1-parameter group s -~ T~, To = identity, satisfying for all s 0 T f l = T-s and, for s >-0, T~L+ _ L + . We have to have two further conditions of technical character. (e) Continuity condi...
متن کامل2 00 1 General framework for a portfolio theory with non - Gaussian risks and non - linear correlations
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we give exact formulas for the tails and for the moments and cumulants of the distribution of returns of a portfolio make of arbitrary compositions of these assets. Using combinato...
متن کاملua nt - p h / 02 06 18 8 v 2 2 8 Ju n 20 02 New q - deformed coherent states with an explicitly known resolution of unity
We construct a new family of q-deformed coherent states |z q , where 0 < q < 1. These states are normalizable on the whole complex plane and continuous in their label z. They allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated Stieltjes power-moment problem and expressed in terms of one of the...
متن کامل