References
Baxter, J.R.: A class of ergodic transformations having simple spectrum. Proc. Amer. Math. Soc.27, 275–279 (1971)
Chacon, R.V.: Approximation of transformations with continous spectrum. Pacific J. Math.2, 293–302 (1969)
Chacon, R.V.: Approximation and spectral multiplicity. Lecture Notes in Math. Vol. 160, pp. 18–22. Berlin-Heidelberg-New York: Springer 1970
Girsanov, I.V.: Spectra of dynamical systems generated by stationary Gaussian processes, (in Russian) Dokl. Akad. Nauk SSSR119, 851–853 (1958)
Halmos, P.R., von Neumann, J.: Operator methods in classical mechanics II. Ann. Math.43, 332–350 (1942)
Halmos, P.R.: On automorphisms of compact groups. Bull. AMS,49, 619–624 (1943)
Halmos, P.R.: Lectures on ergodic theory. The Math. Society of Japan, Tokyo 1956
Del Junco, A.: A transformation with simple spectrum which is not rank one. Can J. Math.29, 655–663 (1977)
Katok, A.B., Stepin, A.M.: Approximation of ergodic dynamic systems by periodic transformations. Dokl. Akad. Nauk SSSR171, 1268–1271 (1966); Soviet Math. Dokl.7, 1638–1641 (1966)
Katok, A.B., Stepin, A.M.: Approximations in ergodic theory. Uspekhi Mat. Nauk22, (1967); Russian Math. Surveys22, 77–102 (1967)
Oseledec, V.I.: The spectrum of ergodic automorphisms. Dokl. Akad. Nauk SSSR168, 776–779 (1966)
Rohlin, V.A.: Entropy of a metric automorphism (in Russian). Dokl. Akad. Nauk. SSSR124, 980–983 (1959)
Rohlin, V.A.: New progress in the theory of transformations with invariant measure. Uspekhi Mat. Nauk15, 2–36 (1960); Russian Math. Surveys15, 1–22 (1960)
Rohlin, V.A.: Lectures on the entropy theory of measure preserving transformations. Uspekhi Mat. Nauk22, (1967; Russian Math. Surveys22, (1967)
Schwartzbauer, T.: A general method for approximating measure preserving transformations. Proc. Amer. Math. Soc.24, 643–648 (1970)
Veršik, A.M.: On the theory of normal dynamic systems. Dokl. Akad. Nauk SSSR114, 9–12 (1962); Soviet Math. Dokl.3, 625–628 (1962)
Veršik, A.M.: Spectral and metric isomorphism of some normal dynamical systems. Dokl. Akad. Nauk SSSR114, 255–257 (1962); Soviet Math. Dokl.3, 693–696 (1962)
Von Neumann, J.: Zur Operatorenmethode in der Klassischen Mechanik. Ann. Math.33, 587–642 (1932)
Yuzvinskii, S.A.: Metric automorphisms with a simple spectrum. Dokl. Akad. Nauk SSSR172, 1036–1038 (1967); Soviet Math. Dokl.8, 243–245 (1967)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Robinson, E.A. Ergodic measure preserving transformations with arbitrary finite spectral multiplicities. Invent Math 72, 299–314 (1983). https://doi.org/10.1007/BF01389325
Issue Date:
DOI: https://doi.org/10.1007/BF01389325