Semiflows and semigroups

Edoardo Vesentini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 2, page 75-82
  • ISSN: 1120-6330

Abstract

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Given a compact Hausdorff space K and a strongly continuous semigroup T of linear isometries of the Banach space of all complex-valued, continuous functions on K , the semiflow induced by T on K is investigated. In the particular case in which K is a compact, connected, differentiable manifold, a class of semigroups T preserving the differentiable structure of K is characterized.

How to cite

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Vesentini, Edoardo. "Semiflows and semigroups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.2 (1996): 75-82. <http://eudml.org/doc/244203>.

@article{Vesentini1996,
abstract = {Given a compact Hausdorff space \( K \) and a strongly continuous semigroup \( T \) of linear isometries of the Banach space of all complex-valued, continuous functions on \( K \), the semiflow induced by \( T \) on \( K \) is investigated. In the particular case in which \( K \) is a compact, connected, differentiable manifold, a class of semigroups \( T \) preserving the differentiable structure of \( K \) is characterized.},
author = {Vesentini, Edoardo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Complex extreme point; Markov lattice operator; Cocycle; Banach-Stone theorem; strongly continuous semigroup; semiflow; differentiable manifold; differentiable structure},
language = {eng},
month = {10},
number = {2},
pages = {75-82},
publisher = {Accademia Nazionale dei Lincei},
title = {Semiflows and semigroups},
url = {http://eudml.org/doc/244203},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Vesentini, Edoardo
TI - Semiflows and semigroups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/10//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 2
SP - 75
EP - 82
AB - Given a compact Hausdorff space \( K \) and a strongly continuous semigroup \( T \) of linear isometries of the Banach space of all complex-valued, continuous functions on \( K \), the semiflow induced by \( T \) on \( K \) is investigated. In the particular case in which \( K \) is a compact, connected, differentiable manifold, a class of semigroups \( T \) preserving the differentiable structure of \( K \) is characterized.
LA - eng
KW - Complex extreme point; Markov lattice operator; Cocycle; Banach-Stone theorem; strongly continuous semigroup; semiflow; differentiable manifold; differentiable structure
UR - http://eudml.org/doc/244203
ER -

References

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  1. ARENDT, W., Characterization of positive semigroups on C 0 ⁢ X . In: R. NAGEL (ed.), One-Parameter Semigroups of Positive Operators. Lecture Notes in Mathematics, n. 1184, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo1980, 122-162. Zbl0585.47030MR763347DOI10.1007/BFb0072760
  2. DINI, U., Fondamenti per la teorica delle funzioni di variabili reali. Nistri, Pisa1878; Unione Matematica Italiana, Bologna1990. JFM10.0274.01
  3. DUNFORD, N. - SCHWARTZ, J. T., Linear Operators. Part I. Interscience, New York1958. Zbl0084.10402
  4. NAGEL, R. - SCHLOTTERBECK, U., Basic results on C 0 ⁢ X . In: R. NAGEL (ed.), One-Parameter Semigroups of Positive Operators. Lecture Notes in Mathematics, n. 1184, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo1980, 117-121. Zbl0585.47030
  5. NAGEL, R., On the linear operator approach to dynamical systems. Conf. Sem. Mat. Università Bari, 243, 1991, 93-111. Zbl0796.58049MR1185558
  6. NEWNS, W. F. - WALKER, A. G., Tangent planes to a differentiate manifold. J. London Math. Soc., 31, 1956, 400-407. Zbl0071.15303MR84163
  7. PAZY, A., Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York-Berlin-Heidelberg-Tokyo1983. Zbl0516.47023MR710486DOI10.1007/978-1-4612-5561-1
  8. SAKAI, S., C * -Algebras and W * -Algebras. Springer-Verlag, New York-Heidelberg-Berlin1971. MR442701
  9. VESENTINI, E., On the Banach-Stone theorem. Adv. in Math., 112, 1995, 135-146. Zbl0854.46025MR1321671DOI10.1006/aima.1995.1030
  10. VESENTINI, E., Conservative operators. In: P. MARCELLINI - G. TALENTI - E. VESENTINI (eds.), Topics in Partial Differential Equations and Applications. Marcel Dekker, New York1996, 303-311. Zbl0841.47024MR1371602

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