The $\mathcal {C}$-Borel transform
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- by Frank M. Cholewinski and Deborah Tepper Haimo PDF
- Proc. Amer. Math. Soc. 42 (1974), 445-451 Request permission
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
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D. T. Haimo and F. M. Cholewinski, The Hankel-Borel transform, Les 265 communications individuelles, Congres International des Mathématiciens, Nice, 1970, p. 185.
- Leopoldo Nachbin, An extension of the notion of integral functions of the finite exponential type, An. Acad. Brasil. Ci. 16 (1944), 143–147. MR 10724
- François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 445-451
- MSC: Primary 44A15
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330946-9
- MathSciNet review: 0330946