According to an extension of a classical theorem of Bernstein, due to C. Herz, a function on Rn belonging to a Besov space of appropriate order has an absolutely convergent Fourier transform. We establish extensions of this result to Cartan motion groups, for Besov spaces defined with respect to both isotropic and non-isotropic differences. © 1987, Australian Mathematical Society. All rights reserved.
Gaudry, G., Pini, R. (1987). Motion groups and absolutely convergent Fourier transforms. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 43(3), 385-397 [10.1017/S1446788700029669].
Motion groups and absolutely convergent Fourier transforms
Pini, R
1987
Abstract
According to an extension of a classical theorem of Bernstein, due to C. Herz, a function on Rn belonging to a Besov space of appropriate order has an absolutely convergent Fourier transform. We establish extensions of this result to Cartan motion groups, for Besov spaces defined with respect to both isotropic and non-isotropic differences. © 1987, Australian Mathematical Society. All rights reserved.
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