Communications in Mathematical Analysis

$L^2$-estimates for the Laplace transform along a family of hyperbolas in the right half-plane

Anatoli Merzon and Sergey Sadov

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By Paley-Wiener theory, the Laplace transform of an $L^2$ function on positive semiaxis satisfies $L^2$ estimates uniformly on the family of vertical lines in the right half-plane. The paper gives a generalization: uniform $L^2$ estimates for the Laplace transform remain valid on a family of hyperbolas in the right half-plane.

Article information

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

First available in Project Euclid: 25 February 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 44A10: Laplace transform

Laplace transform $L^2$ estimates hyperbola Paley-Wiener theory Poisson integral


Sadov, Sergey; Merzon, Anatoli. $L^2$-estimates for the Laplace transform along a family of hyperbolas in the right half-plane. Commun. Math. Anal. (2011), no. 3, 204--208.

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