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Riesz basis of exponential family for a hyperbolic system

  • Abdelkader Intissar , Aref Jeribi and Ines Walha EMAIL logo
Published/Copyright: May 29, 2019

Abstract

This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. It is shown that the associated linear system is the infinitesimal generator of a C0-semigroup; its spectrum consists of zeros of a sine-type function, and its exponential system {eλnt}n1 constitutes a Riesz basis in L2[0,T]. Furthermore, by the spectral analysis method, it is also shown that the linear system has a sequence of eigenvectors, which form a Riesz basis in Hilbert space, and hence the spectrum-determined growth condition is deduced.

Acknowledgements

The authors would like to thank the referees for their valuable suggestions for the revision of the paper and for attracting the authors’ attention to [16].

References

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Received: 2017-02-14
Revised: 2018-05-29
Accepted: 2018-07-03
Published Online: 2019-05-29
Published in Print: 2019-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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