Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501756 | Journal of Differential Equations | 2005 | 24 Pages |
Abstract
Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. Suppose that A is the generator of a C0 semigroup on a Hilbert space and Ï(A)=Ï1(A)âªÏ2(A) with Ï2(A) is consisted of isolated eigenvalues distributed in a vertical strip. It is proved that if Ï2(A) is separated and for each λâÏ2(A), the dimension of its root subspace is uniformly bounded, then the generalized eigenvectors associated with Ï2(A) form an L-basis. Under different conditions on the Riesz projection, the expansion of a semigroup is studied. In particular, a simple criterion for the generalized eigenvectors forming a Riesz basis is given. As an application, a heat exchanger problem with boundary feedback is investigated. It is proved that the heat exchanger system is a Riesz system in a suitable state Hilbert space.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gen Qi Xu, Siu Pang Yung,