Representation formulas for integrable and entire functions of exponential type. II

@article{Frappier1988RepresentationFF,
  title={Representation formulas for integrable and entire functions of exponential type. II},
  author={C. Frappier},
  journal={Canadian Journal of Mathematics},
  year={1988},
  volume={40},
  pages={1010-1024}
}
  • C. Frappier
  • Published 1988
  • Mathematics
  • Canadian Journal of Mathematics
The function Gyj is a periodic function of a, with period 2. For / = 0 (the general case is obtained by translation) the righthand member of (1) is 2rGyj(l). In the following paper we suppose that / satisfies an additional hypothesis of the form/(x) = O ( |JC|~), for some e > 0, as x —» zboo and we give an integral representation of Gy j(a) which is valid for 0 ^ a ^ 2. More precisely, the Theorems 1, 2 and 3, below, contain formulas giving a representation of Gyj(a) valid respectively for 0… Expand
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