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2016 | 3 | 1 | 68-76
Tytuł artykułu

Vector-valued holomorphic and harmonic functions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Strony
68-76
Opis fizyczny
Daty
otrzymano
2015-11-25
zaakceptowano
2016-03-08
online
2016-04-28
Twórcy
  • Institute of Applied Analysis, University of Ulm, 89069 Ulm, Germany
Bibliografia
  • [1] H. Amann: Elliptic operators with infinite-dimensional state space. J. Evol. Equ 1 (2001), 143–188.
  • [2] W. Arendt, C. Batty, M. Hieber, F. Neubrander: Vector-valued Laplace Transforms and Cauchy Problems. Second edition. Birkhäuser Basel (2011)
  • [3] W. Arendt, A.F.M. ter Elst: From forms to semigroups. Oper. Theory Adv. Appl. 221, 47–69.
  • [4] W. Arendt, N. Nikolski: Vector-valued holomorphic functions revisited. Math. Z. 234 (2000), no. 4, 777–805.
  • [5] W. Arendt, N. Nikolski: Addendum: Vector-valued holomorphic functions revisited. Math. Z. 252 (2006), 687–689.
  • [6] S. Axler; P. Bourdon, W. Ramey: Harmonic Function Theory. Springer, Berlin 1992.
  • [7] J. Bonet, L. Frerick, E. Jordá: Extension of vector-valued holomorphic and harmonic functions. Studia Math. 183 (2007), 225–248.
  • [8] J. Diestel, J.J. Uhl: Vector Measures. Amer. Math. Soc. Providence 1977.
  • [9] K.-G. Grosse-Erdmann: The Borel-Ohada theorem revisited. Habilitationsschrift Hagen 1992.
  • [10] K.-G. Grosse-Erdmann: A weak criterion for vector-valued holomorphy. Math. Proc. Cambridge Philos. Soc. 136 (2004), 399–411.
  • [11] T. Kato: Perturbation Theory for Linear Operators. Springer, Berlin 1995.
  • [12] M. Yu. Kokwin: Sets of Uniqueness for Harmonic and Analytic Functions and diverse Problems for Wave equations. Math. Notes. 97 (2015), 376–383.
  • [13] T. Ransford: Potential Theory in the Complex Plane. London Math. Soc., Cambridge University Press 1995.
  • [14] R. Remmert: Funktionentheorie 2. Springer, Berlin 1992.
  • [15] A. Tonolo: Commemorazione di Giuseppe Vitali. Rendiconti Sem. Matem. Univ. Padova 3 (1932), 37–81.
  • [16] V. Wrobel: Analytic functions into Banach spaces and a new characterisation of isomorphic embeddings.. Proc. Amer. Math. Soc. (1982), 539–543.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_conop-2016-0007
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