Harmonic Analysis and Applications

June 4-8, 2018


"Some aspects of warped time-frequency representations on $R^d$ and associated function spaces"

Holighaus, Nicki

We consider the deformation, or warping, of a translation-invariant system generated by a function $\theta$ on $\mathbb{R}^d$ through a diffeomorphism $\Phi$ as a non-uniform covering of frequency space. The resulting collection of functions is used to construct a time-frequency representation naturally adapted to the frequency progression defined by the given diffeomorphism. Under natural conditions on the diffeomorphism $\Phi$ and the generator $\theta$, the resulting \emph{warped time-frequency system} forms a continuous, tight frame. Under suitable regularity assumptions on $\Phi$, we can associate coorbit and decomposition spaces to the warped time-frequency representations obtained from $\Phi$ and any (suitable) generator $\theta$. This is joint work with Felix Voigtlaender

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