Trace properties of certain damped linear elastic systems | Zendy

David L. Russell | Zendy

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Trace properties of certain damped linear elastic systems

Author(s) -

David L. Russell

Publication year - 2013

Publication title -

evolution equations and control theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.665

H-Index - 19

eISSN - 2163-2480

pISSN - 2163-2472

DOI - 10.3934/eect.2013.2.711

Subject(s) - trace (psycholinguistics) , eigenvalues and eigenvectors , orthonormal basis , operator (biology) , sequence (biology) , simple (philosophy) , linear map , generator (circuit theory) , linear system , type (biology) , mathematical analysis , trace class , mathematics , pure mathematics , physics , geology , hilbert space , quantum mechanics , philosophy , repressor , linguistics , chemistry , genetics , biology , paleontology , biochemistry , power (physics) , epistemology , transcription factor , gene

We study the spectrum of a damped linear elastic system with discrete eigenvalues, showing the relationship between the sum of the real parts of the eigenvalues of the (generally unbounded) generator and the trace of the damping operator, assuming the latter to be a trace type operator. Some relationships between the sequence of eigenvectors and a corresponding orthonormal sequence, constructed by means of a variant of the Gram-Schmidt method, are also explored. A simple hybrid system is presented as an example of application.

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