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.
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