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Statistical and Linear Independence of Binary Random Variables
Xiao-Massey lemma block cipher linear cryptanalysis
2017/5/23
Linear cryptanalysis makes use of statistical models that consider linear approximations over block cipher and random permutation as binary random variables. In this note we show that linear and stati...
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].