Linear Independence of Time Frequency Translates for Special Configurations
نویسنده
چکیده
We prove that for any 4 points in the plane that belong to 2 parallel lines, there is no linear dependence between the associated time-frequency translates of any nontrivial Schwartz function. If mild Diophantine properties are satisfied, we also prove linear independence in the category of L2(R) functions.
منابع مشابه
Linear Independence of Time-frequency Translates in R
We establish the linear independence of time-frequency translates for functions f on R having one sided decay limx∈H, |x|→∞ |f(x)|ec|x| log |x| = 0 for all c > 0, which do not vanish on an affine half-space H ⊂ R.
متن کاملLinear Independence of Time-frequency Translates of Functions with Faster than Exponential Decay
We establish the linear independence of time-frequency translates for functions f having one sided decay limx→∞ |f(x)|e log x = 0 for all c > 0. We also prove such results for functions with faster than exponential decay, i.e., limx→∞ |f(x)|e = 0 for all c > 0, under some additional restrictions.
متن کاملLinear Independence of the Integer Translates of Compactly Supported Distributions and Reenable Vectors
Some necessary and suucient conditions in time domain for the global and local linear independence of the integer translates of compactly supported distributions and reenable vectors are established in this paper.
متن کاملProof of the Hrt Conjecture for (2,2) Configurations
We prove that for any 4 points in a (2-2) configuration, there is no linear dependence between the associated time-frequency translates of any L(R) function.
متن کاملA Necessary and Sufficient Condition for the Linear Independence of the Integer Translates of a Compactly Supported Distribution
Given a multivariate compactly supported distribution φ, we derive here a necessary and sufficient condition for the global linear independence of its integer translates. This condition is based on the location of the zeros of φ̂ = The Fourier-Laplace transform of φ. The utility of the condition is demonstrated by several examples and applications, showing in particular, that previous results on...
متن کامل