time 
The proof is based on a variant of Moser's method using timedependent vector fields.


We present twosided singular value estimates for a class of convolutionproduct operators related to timefrequency localization.


The BalianLow theorem (BLT) is a key result in timefrequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(tna)\}_{m,n \in \mbox{\bf Z}}$


Gabor TimeFrequency Lattices and the WexlerRaz Identity


Gabor timefrequency lattices are sets of functions of the form $g_{m \alpha , n \beta} (t) =e^{2 \pi i \alpha m t}g(tn \beta)$ generated from a given function $g(t)$ by discrete translations in time and frequency.


They are potential tools for the decomposition and handling of signals that, like speech or music, seem over short intervals to have welldefined frequencies that, however, change with time.


Often, the Dyadic Wavelet Transform is performed and implemented with the Daubechies wavelets, the BattleLemarie wavelets, or the splines wavelets, whereas in continuoustime wavelet decomposition a much larger variety of mother wavelets is used.


HighOrder Orthonormal Scaling Functions and Wavelets Give Poor TimeFrequency Localization


For a fairly general class of orthonormal scaling functions and wavelets with regularity exponents n, we prove that the areas of the timefrequency windows tend to infinity as n → ∞.


We present an explicit, straightforward construction of smooth integrable functions with prescribed gaps around the origin in both time and frequency domain.


We study boundary value problems for the timeharmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the threedimensional Euclidean space.


We study boundary value problems for the timeharmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the threedimensional Euclidean space.


From the original framer to presentday timefrequency and timescale frames


Equations with two time scales (refinement equations or dilation equations) are central to wavelet theory.


We give strong evidence that the analog of finite propagation for the wave equation does not hold because of inconsistent scaling behavior in space and time.


Using methods developed for phase retrieval problems, we give here a partial answer for some classes of time limited (compactly supported) signals.


In this note we consider continuoustime WeylHeisenberg (Gabor) frame expansions with rational oversampling.


The lowfrequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series.


We also obtain a way of constructing an arbitrary number of nonGaussian continuous time processes whose second order properties are the same as those of fractional Brownian motion.


Finally, we consider the spline of order 2; we investigate numerically the region of the timefrequency plane where it generates a frame and we compute the dual function for some values of the parameters.

