Weakly almost periodic functions on semisimple Lie groups
Tóm tắt
IfG is a semisimple analytic group with finite center, it is proved thatG admits only the “obvious” weakly almost periodic functions. The analysis yields also an intrinsic proof of Moore's ergodicity theorem [7].
Tài liệu tham khảo
De Leeuw, K., andI. Glicksberg: Applications of almost periodic compactifications. Acta Math.105, 63–67 (1961).
Eberlein, W. F.: Abstract ergodic theorems and weakly almost periodic functions. Trans. Amer. Math. Soc.67, 217–240 (1949).
Godement, R.: Les fonctions de type positif et la théorie des groupes. Trans. Amer. Math. Soc.63, 1–84 (1948).
Grothendieck, A.: Critères de compacité dans les espaces fonctionnels généraux. Amer. J. Math.74, 168–186 (1952).
Helgason, S.: Differential Geometry and Symmetric Spaces. New York: Academic Press. 1962.
Moore, C.: Compactifications of symmetric spaces. Amer. J. Math.86, 201–218 (1964).
Moore, C.: Ergodicity of flows on homogeneous spaces. Amer. J. Math.88, 154–178 (1966).
Ryll-Nardzewski, C.: On fixed points of semigroups of endomorphisms of linear spaces. Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), vol. II: Contributions to Probability Theory, part I, pp. 55–61. Berkeley, Calif: Univ. of California Press. 1967.
Veech, W. A.: A fixed point theorem free approach to weak almost periodicity. Trans. Amer. Math. Soc.177, 353–362 (1973).
Warner, G.: Harmonic Analysis on Semi-Simple Lie Groups. Vols. I and II. Berlin-Heidelberg-New York: Springer. 1972.