22,377 research outputs found
Characterization and computation of canonical tight windows for Gabor frames
Let be a Gabor frame for for given window .
We show that the window that generates the canonically
associated tight Gabor frame minimizes among all windows
generating a normalized tight Gabor frame. We present and prove versions of
this result in the time domain, the frequency domain, the time-frequency
domain, and the Zak transform domain, where in each domain the canonical
is expressed using functional calculus for Gabor frame operators. Furthermore,
we derive a Wiener-Levy type theorem for rationally oversampled Gabor frames.
Finally, a Newton-type method for a fast numerical calculation of \ho is
presented. We analyze the convergence behavior of this method and demonstrate
the efficiency of the proposed algorithm by some numerical examples
Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise
correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho
and the spatial dimension d. By means of a stochastic Cole-Hopf transformation,
the critical and correction-to-scaling exponents at the roughening transition
are determined to all orders in a (d - d_c) expansion. We also argue that there
is a intriguing possibility that the rough phases above and below the lower
critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead
to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett.
style files included; slightly expanded reincarnatio
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