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Our proofs proceed in the time domain and allow us to represent each solution regardless of the spectral radius of P(0):=2-s∑cα, which has been a difficulty in previous investigations of this nature.
      
Such systems play an important role in time-frequency analysis and digital signal processing.
      
We study time-continuous Gabor frame generating window functions g satisfying decay properties in time and/or frequency with particular emphasis on rational time-frequency lattices.
      
Using a Whitney decomposition in the Fourier plane, a general bilinear operator is represented as infinite discrete sums of time-frequency paraproducts obtained by associating wave-packets with tiles in phase-plane.
      
Boundedness for the general bilinear operator then follows once the corresponding Lp-boundedness of time-frequency paraproducts has been established.
      
Lp-Boundedness for Time-Frequency Paraproducts, II
      
A Time Domain Characterization of the Fine Local Regularity of Functions
      
Time Decay and Regularity of Solutions to the Wave Equation
      
Time-Frequency Mean and Variance Sequences of Orthonormal Bases
      
Hence, the wavelets used in [23] have a good time frequency localization.
      
We discuss the linear independence of systems ofmvectors in n-dimensional complex vector spaces where the m vectors are time-frequency shifts of one generating vector.
      
More generally, these results apply both to Gabor frames and to systems of Gabor molecules, whose elements share only a common envelope of concentration in the time-frequency plane.
      
We study the composition of time-frequency localization operators (wavepacket operators) and develop a symbolic calculus of such operators on modulation spaces.
      
The use of time-frequency methods (phase space methods) allows the use of rough symbols of ultra-rapid growth in place of smooth symbols in the standard classes.
      
A physical implication is that the corresponding wave function ψ(t, x) = e-itHf(x) admits appropriate time decay in the Besov space scale.
      
Recent applied literature introduces the Stockwell transform (S-transform) as a new approach to time-frequency analysis.
      
A new construction of tight frames for $L_2({\Bbb R}^d)$ with flexible time-frequency localization
      
The iterations, initially formulated for time-continuous Gabor systems, are considered and tested in a discrete setting in which one passes to the appropriately sampled-and-periodized windows and frame operators.
      
The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis.
      
Inversion of the Short-Time Fourier Transform Using Riemannian Sums
      
 

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