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L²-estimates for the Laplace transform along a family of hyperbolas in the right half-plane

Commun. Math. Anal. Conf.
Conference 3 (2011), 204 - 208

L²-estimates for the Laplace transform along a family of hyperbolas in the right half-plane

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Abstract

By Paley-Wiener theory, the Laplace transform of an L2 function on positive semiaxis satisfies L2 estimates uniformly on the family of vertical lines in the right half-plane. The paper gives a generalization: uniform L2 estimates for the Laplace transform remain valid on a family of hyperbolas in the right half-plane.