Perturbations of bi-continuous cosine families
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https://doi.org/10.17398/Palabras clave:
cosine families, non-strongly continuous cosine families, bi-continuous semigroups, perturbationsResumen
In this paper we prove a bounded perturbation theorem for bi-continuous cosine families. We also apply our results to adjoints of strongly continuous cosine families.
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[1] W. Arendt, C.J.K. Batty, Rank-1 perturbations of cosine functions and semigroups, J. Funct. Anal. 238 (1) (2006), 340 – 352.
[2] C. Budde, Positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces, Acta Sci. Math. (Szeged) 87 (3-4) (2021), 571 – 594.
[3] C. Budde, Positive Miyadera-Voigt perturbations of bi-continuous semigroups, Positivity 25 (3) (2021), 1107 – 1129.
[4] C. Budde, On bi-continuous cosine families, Quaest. Math. 47 (8) (2024), 1589 – 1611.
[5] C. Budde, “Bi-continuous operator semigroups–from theory to applications”, Frontiers in Mathematics, Birkhäuser/Springer, Cham, 2026.
[6] C. Budde, B. Farkas, A Desch-Schappacher perturbation theorem for bi-continuous semigroups, Math. Nachr. 293 (6) (2020), 1053 – 1073.
[7] J.B. Cooper, “Saks spaces and applications to functional analysis”, Notas Mat., 64, North-Holland Publishing Co., Amsterdam-New York, 1978.
[8] F. Duan, G. Sun, Bi-continuous cosine operator functions and the generation theorem, Journal of Anhui University of Technology and Science 21 (1) (2006), 55 – 60.
[9] A. Es-Sarhir, B. Farkas, Perturbation for a class of transition semigroups on the Hölder space Cb,loc (H), J. Math. Anal. Appl. 315 (2) (2006), 666 – 685.
[10] B. Farkas, “Perturbations of bi-continuous semigroups”, PhD thesis, Eötvös Loránd University, 2003.
[11] B. Farkas, Perturbations of bi-continuous semigroups, Studia Math. 161 (2) (2004), 147 – 161.
[12] H.O. Fattorini, “Second order linear differential equations in Banach spaces”, North-Holland Math. Stud., 108, North-Holland Publishing Co., Amsterdam, 1985.
[13] H. Komatsu, Semi-groups of operators in locally convex spaces, J. Math. Soc. Japan 16 (1964), 230 – 262.
[14] F. Kühnemund, A Hille-Yosida theorem for bi-continuous semigroups, Semigroup Forum 67 (2) (2003), 205 – 225.
[15] C. Lizama, Uniform continuity and compactness for resolvent families of operators, Acta Appl. Math. 38 (2) (1995), 131 – 138.
[16] H.P. Lotz, Uniform convergence of operators on L∞ and similar spaces, Math. Z. 190 (1985), 207 – 220.
[17] D. Lutz, On bounded time-dependent perturbations of operator cosine functions, Aequationes Math. 23 (1981), 197 – 203.
[18] D. Lutz, Über die Konvergenz operatorwertiger Cosinusfunktionen mit gestörtem infinitesimalen Erzeuger, Period. Math. Hung. 14 (1983), 101 – 105.
[19] C. Palencia, S. Piskarev, On multiplicative perturbations of C0 -groups and C0 -cosine operator functions, Semigroup Forum 63 (2) (2001), 127 – 152.
[20] W. Rudin, “Functional analysis”, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973.
[21] S.-Y. Shaw, On w∗ -continuous cosine operator functions, J. Funct. Anal. 66 (1986), 73 – 95.
[22] M. Shimizu, I. Miyadera, Perturbation theory for cosine families on Banach spaces, Tokyo J. Math. 1 (1978), 333 – 343.
[23] M. Sova, Cosine operator functions, Rozprawy Mat. 49 (1966), 47 pp.
[24] T. Takenaka, N. Okazawa, A Phillips-Miyadera type perturbation theorem for cosine functions of operators, Tohoku Math. J. (2) 30 (1) (1978), 107 – 115.
[25] C.C. Travis, G.F. Webb, Perturbation of strongly continuous cosine family generators, Colloq. Math. 45 (1981), 277 – 285.
[26] X.M. Xue, Perturbations of cosine operator functions, Nanjing Daxue Xuebao Shuxue Bannian Kan 10 (1) (1993), 93 – 98.
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Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
