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On Fourier-Stieltjes Transforms

  • A. P. Calderón (a1) and A. Devinatz (a1)

Extract

Let be the class of bounded non-decreasing functions defined on the real line which are normalized by the conditions ϕ(− ∞) = 0 , ϕ(t + 0) = ϕ(t).

Let be the class of Fourier-Stieltjes transforms of elements of i.e. the elements of and are connected by the relation

where ϕ ∊ and Φ ∊ .It is well known, and easy to verify that this mapping from to is one to one (1, p. 67, Satz 18).

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Copyright

References

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1. Bochner, S., Vorlesungen über Fouriersche Integrale (Leipzig, 1932).
2. Caratheodory, C., Vorlesungen über reelle Funktionen (Leipzig und Berlin, 1918).
3. Dyson, F. J., Fourier transforms of distribution functions, Can. J. Math., 5 (1953), 554558.
4. Saks, S., Theory of the integral (New York, 1937).
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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