APPLICATIONS OF HILBERT SPACE DISSIPATIVE NORM
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The concept of Hilbert space dissipative norm was introduced in [8] to obtain necessary and sufficient conditions for exponential stabil-ity of contraction semigroups. In the present paper we show that the same concept can also be used to derive further properties of contraction semigroups, as well as to characterize strongly stable semigroups that are not exponentially stable.
Abstract
The concept of Hilbert space dissipative norm was introduced in [8] to obtain necessary and sufficient conditions for exponential stabil-ity of contraction semigroups. In the present paper we show that the same concept can also be used to derive further properties of contraction semigroups, as well as to characterize strongly stable semigroups that are not exponentially stable.
참고문헌 (11)
- K. N. Boyadzhiev, "Strong stability of Hilbert space contraction semigroups", Studia Sci. Math. Hungar, 30(3), pp.165~182 (1995)
- R. Chill, "Stability of operator semigroups: ideas and results, Perspectives in operator theory", Banach Center Publ., 75, pp.71~109 (2007), Polish Acad. Sci.
- R. Datko, "Extending a theorem of A.M. Liapunov to Hilbert space", J. Math. Anal. Appl, 32, pp.610~616 (1970)
- R. Datko, "Uniform asymptotic stability of evolutionary process in a Banach space", SIAM J. Math. Anal, 3, pp.428~445 (1972)
- P. A. Fillmore, "Notes on Operator Theory" (1970), Van Nostrand
- J. A. Goldstein, "Semigroups of Linear Operators and Applications" (1985), Oxford University Press
- C. S. Kubrusly, "Proper contractions and invariant subspaces", Int. J. Math. Math. Sci, 28(4), pp.223~230 (2001)
- C. S. Kubrusly, "Stabilities of Hilbert space contraction semigroups revisited", Semigroup Forum, 79(2), pp.341~348 (2009)
- C. S. Kubrusly, "Strong stability for cohyponormal operators", J. Operator Theory, 31(1), pp.123~127 (1994)
- N. Levan, "The stabilizability problem: a Hilbert space operator decomposition approach", IEEE Trans. Circuits and Systems, 25(9), pp.721~727 (1978)
- B. Sz.-Nagy, "Harmonic Analysis of Operators on Hilbert Space" (1970)