Abstract
In this paper we define an interpolation family of transformations, whose extremes are the Gabor and wavelet transformations, in order to extend the Cordoba-Fefferman results (see [CF]) and to define a differential calculus at the first order. This interpolation family is based on the representation through translated and modulated versions of an analyzing function, with the additional property that this family is naturally localized in paraboloids. This will allow us at the end of the paper to construct anisotropic Banach spaces of functions by pullback techniques.
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Nazaret, B., Holschneider, M. (2003). An Interpolation Family between Gabor and Wavelet Transformations. In: Albeverio, S., Demuth, M., Schrohe, E., Schulze, BW. (eds) Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations. Operator Theory: Advances and Applications, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8073-2_7
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DOI: https://doi.org/10.1007/978-3-0348-8073-2_7
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