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Some applications of Fejer's theorem to operator cosine functions in Banach spaces

Authors: Ioana Cioranescu and Carlos Lizama
Journal: Proc. Amer. Math. Soc. 125 (1997), 2353-2362
MSC (1991): Primary 47D09; Secondary 34G10
MathSciNet review: 1389510
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Abstract: We characterize spectral properties of operator cosine functions in Banach spaces in terms of the Césaro summability of two series associated to the resolvent of the corresponding infinitesimal generator.

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  • 1. I. Cioranescu, C. Lizama, Spectral properties of cosine operator functions, Aequationes Math. 36 (1988) 80-98. MR 89i:47071
  • 2. V.I. Gorbachuk, A.V. Knyazyuk, Boundary values of solutions of operator-differential equations, Russian Math. Surveys 44:3 (1989) 67-111. MR 91c:47080
  • 3. G. Greiner, A short proof of Gearhart's theorem, Semesterbericht Funktionalanalysis Tubingen SS 89 16 (1989) 89-92.
  • 4. G. Greiner, M. Schwarz, Weak spectral mapping theorems for functional differential equations, J.Diff. Eq. 94 (1991) 205-216. MR 92k:47079
  • 5. Y. Katznelson, Harmonic Analysis, New York-London-Sydney-Toronto, 1968. MR 40:1734
  • 6. Y. Latushkin, S. Montgomery-Smith, Lyapunov theorems for Banach spaces, Bull. Amer. Math. Soc. (New series) 31 (1994) 44-49. MR 94j:47062
  • 7. C. Lizama, On the spectrum of cosine operator functions, Int. Eq. Operator Theory 12 (1989) 713-724. MR 90h:47074
  • 8. R.Nagel, One-Parameter Semigroups of Positive Operators, Lecture Notes in Mathematics, Vol. 1184, Springer-Verlag, Berlin/New York, 1980. MR 88i:47022
  • 9. B. Nagy, On cosine operator functions in Banach spaces, Acta Sci. Math. (Szeged) 36 (1974) 281-290. MR 51:11191
  • 10. C.C. Travis, G.F. Webb, Cosine families and abstract non-linear second order differential equations, Acta Math. Acad. Sci. Hung. 32 (1978) 75-96. MR 58:17404

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Additional Information

Ioana Cioranescu
Affiliation: Department of Mathematics, University of Puerto Rico, Box 23355 Rio Piedras, Puerto Rico 00931

Carlos Lizama
Affiliation: Departamento de Matemática y C. C., Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile

Received by editor(s): December 11, 1995
Received by editor(s) in revised form: February 22, 1996
Additional Notes: This research was done while the first author was visiting the Department of Mathematics, University of Santiago de Chile, supported by CONICYT
The second author was partially supported by FONDECYT grant 1930066 and DICYT (USACH)
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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