time 
Our proofs proceed in the time domain and allow us to represent each solution regardless of the spectral radius of P(0):=2s∑cα, which has been a difficulty in previous investigations of this nature.


Such systems play an important role in timefrequency analysis and digital signal processing.


We study timecontinuous Gabor frame generating window functions g satisfying decay properties in time and/or frequency with particular emphasis on rational timefrequency lattices.


Using a Whitney decomposition in the Fourier plane, a general bilinear operator is represented as infinite discrete sums of timefrequency paraproducts obtained by associating wavepackets with tiles in phaseplane.


Boundedness for the general bilinear operator then follows once the corresponding Lpboundedness of timefrequency paraproducts has been established.


LpBoundedness for TimeFrequency Paraproducts, II


A Time Domain Characterization of the Fine Local Regularity of Functions


Time Decay and Regularity of Solutions to the Wave Equation


TimeFrequency 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 ndimensional complex vector spaces where the m vectors are timefrequency 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 timefrequency plane.


We study the composition of timefrequency localization operators (wavepacket operators) and develop a symbolic calculus of such operators on modulation spaces.


The use of timefrequency methods (phase space methods) allows the use of rough symbols of ultrarapid growth in place of smooth symbols in the standard classes.


A physical implication is that the corresponding wave function ψ(t, x) = eitHf(x) admits appropriate time decay in the Besov space scale.


Recent applied literature introduces the Stockwell transform (Stransform) as a new approach to timefrequency analysis.


A new construction of tight frames for $L_2({\Bbb R}^d)$ with flexible timefrequency localization


The iterations, initially formulated for timecontinuous Gabor systems, are considered and tested in a discrete setting in which one passes to the appropriately sampledandperiodized windows and frame operators.


The Density Theorem for Gabor Frames is one of the fundamental results of timefrequency analysis.


Inversion of the ShortTime Fourier Transform Using Riemannian Sums

