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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The $ \mathcal{C}$-Borel transform


Authors: Frank M. Cholewinski and Deborah Tepper Haimo
Journal: Proc. Amer. Math. Soc. 42 (1974), 445-451
MSC: Primary 44A15
MathSciNet review: 0330946
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Abstract: For $ \mathcal{C}$, a given entire function, it is established that the $ \mathcal{C}$-Borel transform is a linear isomorphism of the space dual to a space of admissible holomorphic functions on a disk in the complex plane C onto the space of admissible entire functions of certain growth. The theory is extended to $ {C^n}$ and shown to include the Fourier-Borel and Hankel-Borel transforms as special cases.


References [Enhancements On Off] (What's this?)

  • [1] D. T. Haimo and F. M. Cholewinski, The Hankel-Borel transform, Les 265 communications individuelles, Congres International des Mathématiciens, Nice, 1970, p. 185.
  • [2] Leopoldo Nachbin, An extension of the notion of integral functions of the finite exponential type, Anais Acad. Brasil. Ci. 16 (1944), 143–147. MR 0010724 (6,60c)
  • [3] François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131 (37 #726)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0330946-9
PII: S 0002-9939(1974)0330946-9
Article copyright: © Copyright 1974 American Mathematical Society