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THE NONCOMMUTATIVE WIENER LEMMA,LINEAR INDEPENDENCE,AND SPECTRAL PROPERTIES OF THE ALGEBRA OF TIME-FREQUENCY SHIFT OPERATORS
NONCOMMUTATIVE WIENER LEMMA LINEAR INDEPENDENCE SPECTRAL PROPERTIES OF THE ALGEBRA TIME-FREQUENCY SHIFT OPERATORS
2015/9/29
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracia...
Linear independence of time-frequency translates of functions with faster than exponential decay
Gabor system exponential decay HRT conjecture linear independence timefrequency translates analytic zero divisor conjecture
2012/6/29
We establish the linear independence of time-frequency translates for functions $f$ having one sided decay $\lim_{x\to \infty} |f(x)| e^{cx \log x} = 0$ for all $c>0$. We also prove such results for f...
$\ell^2$-Linear Independence for the System of Integer Translates of a Square Integrable Function
Linear Independence Square Integrable Function
2010/11/15
We prove that if the system of integer translates of a square integrable function is $\ell^2$-linear independent then its periodization function is strictly positive almost everywhere. Indeed we show...
LINEAR INDEPENDENCE OF REFINABLEDISTRIBUTIONS SUPPORTED ON[0, 2]×[0, 2]
Refinable distribution symbo
2007/12/11
In this paper a necessary and sufficient condition on symbol is given for linear independence of refinable distributions supported on [0,2]×[0,2].