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DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS

  • Published : 2004.11.01

Abstract

We research properties of analytic functions which are exponentially decreasing or increasing. Also we show that the space of test functions is dense in the space of extended Fourier hyper-functions, and that the Fourier transform of the space of extended Fourier hyperfunctions into itself is an isomorphism and Parseval's inequality holds.

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Cited by

  1. New spaces of functions and hyperfunctions for Hankel transforms and convolutions vol.153, pp.2, 2008, https://doi.org/10.1007/s00605-007-0498-9
  2. THE SPACE OF FOURIER HYPERFUNCTIONS AS AN INDUCTIVE LIMIT OF HILBERT SPACES vol.19, pp.4, 2004, https://doi.org/10.4134/CKMS.2004.19.4.661