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Abstract

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We study the strong continuity of semigroups of composition operators on local Dirichlet spaces.

Keywords

local Dirichlet spacescomposition operatorssemigroups of composition operators

MSC classification

Primary: 47B33: Composition operators
Secondary: 30H05: Bounded analytic functions 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 47D06: One-parameter semigroups and linear evolution equations 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 144 - 154
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Berkson, E. and Porta, H., ‘Semigroups of analytic functions and composition operators’, Michigan Math. J. 25 (1978), 101–115.Google Scholar
Bracci, F., Contreras, M. D. and Díaz-Madrigal, S., ‘Evolution families and the Loewner equation I: the unit disc’, J. reine angew. Math. 672 (2012), 1–37.Google Scholar
Contreras, M. D. and Díaz-Madrigal, S., ‘Analytic flows on the unit disk: angular derivatives and boundary fixed points’, Pacific J. Math. 222 (2005), 253–286.Google Scholar
Contreras, M. D., Díaz-Madrigal, S. and Pommerenke, Ch., ‘Fixed points and boundary behaviour of the Koenigs function’, Ann. Acad. Sci. Fenn. Math. 29 (2004), 471–488.Google Scholar
Contreras, M. D., Díaz-Madrigal, S. and Pommerenke, Ch., ‘On boundary critical points for semigroups of analytic functions’, Math. Scand. 98 (2006), 125–142.Google Scholar
Cowen, C. C. and MacCluer, B. O., Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics (CRC Press, Boca Raton, FL, 1995).Google Scholar
Duren, P. L., Theory of H p -Spaces, Pure and Applied Mathematics, 38 (Academic Press, New York–London, 1970).Google Scholar
Matache, V., ‘Weighted composition operators on H 2 and applications’, Complex Anal. Oper. Theory 2 (2008), 169–197.CrossRefGoogle Scholar
Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44 (Springer, New York, 1983).CrossRefGoogle Scholar
Richter, S., ‘A representation theorem for cyclic analytic two-isometries’, Trans. Amer. Math. Soc. 328 (1991), 325–349.CrossRefGoogle Scholar
Richter, S. and Sundberg, C., ‘A formula for the local Dirichlet integral’, Michigan Math. J. 38 (1991), 355–379.Google Scholar
Sarason, D. and Silva, J.-N. O., ‘Composition operators on a local Dirichlet space’, J. Anal. Math. 87 (2002), 433–450.CrossRefGoogle Scholar
Siskakis, A. G., ‘Composition semigroups and the Cesáro operator on H p ’, J. Lond. Math. Soc. (2) 36 (1987), 153–164.Google Scholar