Some theorems on integrability of Laplace transforms and their applications

Abstract

In this article, we study the Laplace transforms of functions, integrable on with some weight. We obtain two theorems of the Paley–Viener type and apply them to the problem of completeness of systems of exponentials in weighted L ^p spaces on .

Keywords:

• Laplace transform
• Bergman spaces
• Systems of exponentials

Acknowledgements

This work was supported by the Russian Foundation for Basic Research, grant no. 06-01-00326.

Additional information

Notes on contributors

L. Biryukov

Email: [email protected]