Abstract
We describe classes of temperate distributions with prescribed decay properties at infinity. The definition of the elements of such classes is given in terms of the Schwartz’ bounded distributions, and we discuss their characterization in terms of convolution and of decomposition as a finite sum of derivatives of suitable functions. We also prove mapping properties under the action of a class of Fourier integral operators, with inhomogeneous phase function and polynomially bounded symbol globally defined on \(\mathbb{R}^d\)
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© 2017 Springer International Publishing AG
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Ascanelli, A., Coriasco, S., Süß, A. (2017). On Temperate Distributions Decaying at Infinity. In: Oberguggenberger, M., Toft, J., Vindas, J., Wahlberg, P. (eds) Generalized Functions and Fourier Analysis. Operator Theory: Advances and Applications(), vol 260. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51911-1_1
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DOI: https://doi.org/10.1007/978-3-319-51911-1_1
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-51910-4
Online ISBN: 978-3-319-51911-1
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