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Certain isometries related to the bilateral laplace transform

    S. B. Yakubovich Affiliation

Abstract

We study certain isometries between Hilbert spaces, which are generated by the bilateral Laplace transform



In particular, we construct an analog of the Bargmann‐Fock type reproducing kernel Hilbert space related to this transformation. It is shown that under some integra‐bility conditions on $ the Laplace transform FF(z), z = x + iy is an entire function belonging to this space. The corresponding isometrical identities, representations of norms, analogs of the Paley‐Wiener and Plancherel's theorems are established. As an application this approach drives us to a different type of real inversion formulas for the bilateral Laplace transform in the mean convergence sense.


First Published Online: 14 Oct 2010

Keyword : bilateral Laplace transform, Hilbert space, Sobolev space, real inversion formula, Fourier transform, Hermite polynomials, Bargmann transform, Plancherel theorem

How to Cite
Yakubovich, S. B. (2006). Certain isometries related to the bilateral laplace transform. Mathematical Modelling and Analysis, 11(3), 331-346. https://doi.org/10.3846/13926292.2006.9637321
Published in Issue
Sep 30, 2006
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