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Weak convergence of inner superposition operators
Author(s):
Mikhail
E.
Drakhlin;
Eugene
Stepanov
Journal:
Proc. Amer. Math. Soc.
126
(1998),
173-179.
MSC (1991):
Primary 47B38, 47A67, 34K05
MathSciNet review:
1403121
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Abstract:
The equivalence of the weak (pointwise) and strong convergence of a sequence of inner superposition operators is proved as well as the criteria for such convergence are provided. Besides, the problems of continuous weak convergence of such operators and of representation of a limit operator are studied.
References:
- 1.
- N. V. Azbelev, V. P. Maksimov, and L.F. Rakhmatullina. Introduction to the Theory of Functional Differential Equations. ``Nauka'', Moscow, 1991. in Russian. MR 92j:34123
- 2.
- G. Buttazzo and L. Freddi. Optimal control problems with weakly converging input operators. Discrete and Continuous Dynamical Systems, 1(3):401-420, 1995. MR 97b:49016
- 3.
- C. Kuratowski. Topologie, volume 1. Pa\'{n}stwowe Wydawnictwo Naukowe, Warszawa, 1958. in French. MR 19:873d
- 4.
- M.E. Drakhlin. On convergence of sequences of internal superposition operators. Functional Differential Equations. Israel Seminar, 1:83-94, 1993. MR 95g:47047
- 5.
- M.E. Drakhlin. An inner superposition operator in the spaces of summable functions. Izvestiya VUZ. Matematika, 30(5):18-24, 1986. in Russian. MR 88b:47039
- 6.
- Lusternik L. A. and Sobolev V. I. Short Course of Functional Analysis. Vyschaya Shkola, Moscow, 1982. in Russian.
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Additional Information:
Mikhail
E.
Drakhlin
Affiliation:
Research Institute, College of Judea and Samaria, Kedumim-Ariel, D.N. Efraim 44820, Israel
Eugene
Stepanov
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
Email:
stepanov@cibs.sns.it
DOI:
10.1090/S0002-9939-98-03949-5
PII:
S 0002-9939(98)03949-5
Received by editor(s):
October 23, 1995
Received by editor(s) in revised form:
July 3, 1996
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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