논문KCI 등재
Exponential stability of infinite dimensional linear systems
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회논문집 (Communications of the KMS)|제31권 제3호|pp. 603-611
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초록
In this paper, we show that if ${\mathcal A}$ is a differential subalgebra of Banach algebras ${\mathcal B}(\ell^r)$, $1\le r\le \infty$, then solutions of the infinite dimensional linear system associated with a matrix in ${\mathcal A}$ have its $p$-exponential stability being equivalent to each other for different $1\le p\le \infty$.
Abstract
In this paper, we show that if ${\mathcal A}$ is a differential subalgebra of Banach algebras ${\mathcal B}(\ell^r)$, $1\le r\le \infty$, then solutions of the infinite dimensional linear system associated with a matrix in ${\mathcal A}$ have its $p$-exponential stability being equivalent to each other for different $1\le p\le \infty$.
참고문헌 (13)
- R. F. Curtain, "An Introduction to Infinite Dimensional Linear Systems Theorey" (1995), Springer-Verlag
- K. Grochenig, "Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis" (2010), Birkhauser
- K. Grochenig, "Noncommutative approximation: inverse-closed subalgebras and off-diagonal decay of matrices", Constr. Approx, 32(3), pp.429~466 (2010)
- K. Grochenig, "Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices", Trans. Amer. Math. Soc, 358, pp.2695~2711 (2006)
- M. Hirsch, "Differential Equations, Dynamical Systems, and Linear Alge-bra" (1974), Academic Press
- I. Krishtal, "Wiener’s lemma: pictures at exhibition", Rev. Un. Mat. Argentina, 52(2), pp.61~79 (2011)
- N. Motee, "Optimal control of spatially distributed systems", IEEE Trans. Automat. Control, 53(7), pp.1616~1629 (2008)
- N. Motee, "Sparsity measures for spatially decaying systems", arXiv:1402.4148, ~
- C. E. Shin, "Infinite matrices with subpolynomial off-diagonal decay", ~
- C. E. Shin, "Wiener’s lemma: localization and various approaches", Appl. Math. J. Chinese Univ. Ser. B, 28(4), pp.465~484 (2013)
- Q. Sun, "Wiener’s lemma for infinite matrices with polynomial off-diagonal decay", C. R. Math. Acad. Sci. Paris, 340(8), pp.567~570 (2005)
- Q. Sun, "Wiener’s lemma for infinite matrices", Trans. Amer. Math. Soc, 359(7), pp.3099~3123 (2007)
- Q. Sun, "Wiener’s lemma for infinite matrices II", Constr. Approx, 34(2), pp.209~235 (2011)
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