On the singularities of continuous Legendre transforms

Authors:
Gilbert G. Walter and Ahmed I. Zayed

Journal:
Proc. Amer. Math. Soc. **97** (1986), 673-681

MSC:
Primary 44A15

DOI:
https://doi.org/10.1090/S0002-9939-1986-0845986-9

MathSciNet review:
845986

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Abstract | References | Similar Articles | Additional Information

Abstract: The analytic properties of continuous Legendre transform of a function holomorphic in an elliptical neighborhood of the real interval are investigated. It is shown to be an entire function of exponential type whose Borel transform has a singularity at if and only if has one at where . The proof involves a modification of "Hadamard's argument" on multiplication of singularities. The result may also be interpreted as a statement about the second continuous Legendre transform which gives in terms of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0845986-9

Keywords:
Continuous Legendre transforms,
singularities,
analytic continuation

Article copyright:
© Copyright 1986
American Mathematical Society