A class of quasicontractive semigroups acting on Hardy and Dirichlet space

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• 作者：C. Avicou ; I. Chalendar ; J. R. Partington
• 关键词：Primary ; 47D03 ; 47B33 ; Secondary ; 47B44 ; 30H10 ; Strongly continuous semigroup ; Hardy space ; Dirichlet space ; Quasicontractive semigroup ; Composition operators
• 刊名：Journal of Evolution Equations
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：15
• 期：3
• 页码：647-665
• 全文大小：511 KB
• 参考文献：1.M. Abate, The infinitesimal generators of semigroups of holomorphic maps. Ann. Mat. Pura Appl. 161 (1992), no. 4, 167鈥?80.
  2.D. Aharonov, S. Reich, and D. Shoikhet, Flow invariance conditions for holomorphic mappings in Banach spaces. Math. Proc. R. Ir. Acad. 99A (1999), no. 1, 93鈥?04.
  3.L.V. Ahlfors, Conformal invariants: topics in geometric function theory. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Co., New York-D眉sseldorf-Johannesburg, 1973.
  4.M. Bakonyi and T. Constantinescu, Schur鈥檚 algorithm and several applications. Pitman Research Notes in Mathematics Series, 261. Longman Scientific & Technical, Harlow, 1992.
  5.E. Berkson and H. Porta, Semigroups of analytic functions and composition operators. Michigan Math. J. 25 (1978), no. 1, 101鈥?15.
  6.I. Chalendar and J.R. Partington, Norm estimates for weighted composition operators on spaces of holomorphic functions. Complex Anal. Oper. Theory 8 (2014), no. 5, 1087鈥?095.
  7.C.C. Cowen and B.D. MacCluer, Composition operators on spaces of analytic functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995.
  8.O. El-Fallah, K. Kellay, J. Mashreghi and T. Ransford, A primer on the Dirichlet space. Cambridge Tracts in Mathematics, 203. Cambridge University Press, Cambridge, 2014.
  9.K.-J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations. Springer-Verlag, New York, 2000.
  10.J.B. Garnett, Bounded analytic functions. Graduate Texts in Mathematics, 236. Revised first edition. Springer, 2010.
  11.Martin M.J., Vukoti膰 D.: Norms and spectral radii of composition operators on the Dirichlet space. J. Math.Anal. Appl. 304, 22鈥?2 (2005)MATH MathSciNet CrossRef
  12.J.R. Partington, Interpolation, identification, and sampling. London Mathematical Society Monographs. New Series, 17. The Clarendon Press, Oxford University Press, New York, 1997.
  13.A. Pazy, Semigroups of linear operators and applications to partial differential equations. Applied mathematical Sciences, 44. Springer, 1983.
  14.I. Schur, 脺ber Potenzreihen, die im Innern des Einheitskreises beschr盲nkt sind J. Reine Angew. Math. 147 (1917), 205鈥?32. English translation in: I. Schur Methods in Operator Theory and Signal Processing, I. Gohberg, ed., Birkh盲user, 1986, 31鈥?9.
  15.D. Shoikhet, Semigroups in geometrical function theory. Kluwer Academic Publishers, Dordrecht, 2001.
  16.Siskakis A.G.: Semigroups of composition operators on the Dirichlet space. Results Math. 30, 165鈥?73 (1996)MATH MathSciNet CrossRef
  17.A.G. Siskakis, Semigroups of composition operators on spaces of analytic functions, a review. Studies on composition operators (Laramie, WY, 1996), 229鈥?52, Contemp. Math., 213, Amer. Math. Soc., Providence, RI, 1998.
  
• 作者单位：C. Avicou (1)
  I. Chalendar (1)
  J. R. Partington (2)
  
  1. I. C. J., UFR de Math茅matiques, Universit茅 Lyon 1, 43 bld. du 11/11/1918, 69622, Villeurbanne Cedex, France
  2. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1424-3202

文摘

This paper provides a complete characterization of quasicontractive C ₀-semigroups on Hardy and Dirichlet space with a prescribed generator of the form \({Af=Gf^\prime}\) . We show that such semigroups are semigroups of composition operators, and we give simple sufficient and necessary condition on G. Our techniques are based on ideas from semigroup theory, such as the use of numerical ranges. Mathematics Subject Classification Primary: 47D03 47B33 Secondary: 47B44 30H10