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The proof is based on a variant of Moser's method using time-dependent vector fields.
      
We present two-sided singular value estimates for a class of convolution-product operators related to time-frequency localization.
      
The Balian-Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(t-na)\}_{m,n \in \mbox{\bf Z}}$
      
Gabor Time-Frequency Lattices and the Wexler-Raz Identity
      
Gabor time-frequency lattices are sets of functions of the form $g_{m \alpha , n \beta} (t) =e^{-2 \pi i \alpha m t}g(t-n \beta)$ 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 well-defined frequencies that, however, change with time.
      
Often, the Dyadic Wavelet Transform is performed and implemented with the Daubechies wavelets, the Battle-Lemarie wavelets, or the splines wavelets, whereas in continuous-time wavelet decomposition a much larger variety of mother wavelets is used.
      
High-Order Orthonormal Scaling Functions and Wavelets Give Poor Time-Frequency Localization
      
For a fairly general class of orthonormal scaling functions and wavelets with regularity exponents n, we prove that the areas of the time-frequency 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 time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
From the original framer to present-day time-frequency and time-scale 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 continuous-time Weyl-Heisenberg (Gabor) frame expansions with rational oversampling.
      
The low-frequency 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 non-Gaussian 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 time-frequency plane where it generates a frame and we compute the dual function for some values of the parameters.
      
 

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