Abstract
The concept of the asymptotic resolvent of an operator is introduced and used to establish theorems on the generation of semigroups of distributions and operator semigroups of class (ℒ ploc , ℬ) in a locally convex space.
Similar content being viewed by others
Literature cited
Yu. M. Vuvunikyan, “Generation of semigroups of endomorphism distributions of a convex space,” Dokl. Akad. Nauk SSSR,198, No. 2, 269–272 (1971).
Yu. M. Vuvunikyan, “Evolution representations of the algebras Sα,” Dokl. Akad. Nauk SSSR,215, No. 5, 1035–1037 (1974).
J. L. Lions, “Les semi-groupes distributions,” Port. Math.,19, 141–164 (1960).
T. Ushijima, “Some properties of regular distribution semigroups,” Proc. Jpn. Acad.,45, No. 4, 224–227 (1969).
J. L. Lions, “Supports dans la transformation de Laplace,” J. Anal. Math.,2, 369–380 (1952/53).
E. Hille and R. Phillips, “Functional Analysis and Semigroups,” Colloquium Publ. Am. Math. Soc. (1957).
T. Romura, “Semigroups of operators in locally convex spaces,” J. Function. Anal.,2, No. 3, 258–296 (1969).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 433–442, September, 1977.
Rights and permissions
About this article
Cite this article
Vuvunikyan, Y.M. Asymptotic resolvent and theorems on generation of semigroups of operators in locally convex spaces. Mathematical Notes of the Academy of Sciences of the USSR 22, 732–737 (1977). https://doi.org/10.1007/BF02412504
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02412504