{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:38Z","timestamp":1787322938720,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>\n                    This paper gives an abstract sufficient condition on Riesz basis with parentheses property for the generators of C\n                    <jats:sub>0<\/jats:sub>\n                    -groups in Hilbert spaces whose eigenvalues are comprised of some finite unification of separable sets after taking the algebraic multiplicities into account. The condition is then applied to the closed-loop system of a serially connected string system under joint damping feedbacks to show that there is a family of generalized eigenfunctions that form a Riesz basis with parentheses in the state space. The spectrum-determined growth condition is concluded as a consequence.\n                  <\/jats:p>","DOI":"10.1137\/s0363012902420352","type":"journal-article","created":{"date-parts":[[2004,12,9]],"date-time":"2004-12-09T21:00:32Z","timestamp":1102626032000},"page":"1234-1252","source":"Crossref","is-referenced-by-count":25,"title":["A Sufficient Condition on Riesz Basis with Parentheses of Non--Self-Adjoint Operator and Application to a Serially Connected String System under Joint Feedbacks"],"prefix":"10.1137","volume":"43","author":[{"given":"Bao-Zhu","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Xie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","unstructured":"S. A. Avdonin and S. A. 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