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We study the strong continuity of semigroups of composition operators on local Dirichlet spaces.
Berkson, E. and Porta, H., ‘Semigroups of analytic functions and composition operators’, Michigan Math. J.25 (1978), 101–115.Google Scholar
[2]
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
[3]
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
[4]
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
[5]
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
[6]
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
[7]
Duren, P. L., Theory of Hp-Spaces, Pure and Applied Mathematics, 38 (Academic Press, New York–London, 1970).Google Scholar
[8]
Matache, V., ‘Weighted composition operators on H2 and applications’, Complex Anal. Oper. Theory2 (2008), 169–197.CrossRefGoogle Scholar
[9]
Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44 (Springer, New York, 1983).CrossRefGoogle Scholar
[10]
Richter, S., ‘A representation theorem for cyclic analytic two-isometries’, Trans. Amer. Math. Soc.328 (1991), 325–349.CrossRefGoogle Scholar
[11]
Richter, S. and Sundberg, C., ‘A formula for the local Dirichlet integral’, Michigan Math. J.38 (1991), 355–379.Google Scholar
[12]
Sarason, D. and Silva, J.-N. O., ‘Composition operators on a local Dirichlet space’, J. Anal. Math.87 (2002), 433–450.CrossRefGoogle Scholar
[13]
Siskakis, A. G., ‘Composition semigroups and the Cesáro operator on Hp’, J. Lond. Math. Soc. (2)36 (1987), 153–164.Google Scholar