Weak convergence of inner superposition operators

Drakhlin, Mikhail; Stepanov, Eugene

doi:10.1090/S0002-9939-98-03949-5

Weak convergence of inner superposition operators
HTML articles powered by AMS MathViewer

by Mikhail E. Drakhlin and Eugene Stepanov

Proc. Amer. Math. Soc. 126 (1998), 173-179

DOI: https://doi.org/10.1090/S0002-9939-98-03949-5

PDF | Request permission

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

N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Vvedenie v teoriyu funktsional′no-differentsial′nykh uravneniĭ, “Nauka”, Moscow, 1991 (Russian). With an English summary. MR 1144998
Giuseppe Buttazzo and Lorenzo Freddi, Optimal control problems with weakly converging input operators, Discrete Contin. Dynam. Systems 1 (1995), no. 3, 401–420. MR 1355882, DOI 10.3934/dcds.1995.1.401
Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
Michael E. Drakhlin, On convergence of sequences of internal superposition operators, Functional-differential equations, Funct. Differential Equations Israel Sem., vol. 1, Coll. Judea Samaria, Ariel, 1993, pp. 83–94. MR 1297971
M. E. Drakhlin, Inner superposition operator in spaces of integrable functions, Izv. Vyssh. Uchebn. Zaved. Mat. 5 (1986), 18–24, 88 (Russian). MR 854952
Lusternik L. A. and Sobolev V. I. Short Course of Functional Analysis. Vyschaya Shkola, Moscow, 1982. in Russian.