Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 3: 523 - 535

DOI: https://doi.org/10.1007/s11464-013-0276-z

RESEARCH ARTICLE

New point view of spectral gap in functional spaces for birth-death processes

  • Yutao MA ,
  • Yonghua MAO
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  • School of Mathematical Sciences, Key Laboratory on Mathematics and Complex System, Beijing Normal University, Beijing 100875, China

Received date: 17 Aug 2012

Accepted date: 13 Dec 2012

Published date: 24 Jun 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

Constructing some proper functional spaces, we obtain the corresponding norm for the operator (-L)-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5(3): 379-515], for transient birth-death processes.

Key words： Birth-death processes; Dirichlet first eigenvalue; variational formula; spectral theory; duality

Cite this article

Yutao MA , Yonghua MAO . New point view of spectral gap in functional spaces for birth-death processes[J]. Frontiers of Mathematics in China, 2014 , 9(3) : 523 -535 . DOI: 10.1007/s11464-013-0276-z

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