DUALITY FOR AVERAGING METHODS

Joseph Rosenblatt

Received July 25, 2009

References:

[1] V. Bergelson and J. Rosenblatt, Mixing actions of groups, Illinois J. Math. 32(1) (1988), 65-80. [2] G. Birkhoff, Lattice Theory, Vol. 25, 3rd ed., AMS Colloquium Publications, Providence, Rhode Island, 1979. [3] P. M. Cohn, Universal Algebra, Harper & Row, New York, London, 1965. [4] J. L. Kelley, I. Namioka et al., Linear Topological Spaces, D. van Nostrand Co., Princeton, 1963. [5] W. J. Pervin, Foundations of General Topology, Academic Press, New York, 1964. [6] J. Rosenblatt, Norm convergence in ergodic theory and the behavior of Fourier transforms, Canad. J. Math. 46(1) (1994), 184-199. [7] J. Rosenblatt, When the integral is the limit, J. Math. Anal. Appl. 205(2) (1997), 560-567. [8] J. Rosenblatt, Distinguishing transformations by averaging methods, Idris Assani, ed., Proceedings of the 2007-2008 Ergodic Theory Workshops, AMS Contemporary Mathematics, preprint, 18 pages (to appear). [9] W. Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, Vol. 12, Wiley and Sons, New York, 1962. [10] B. P. Smith, Helson sets not containing the identity are uniform Fatou-Zygmund sets, Indiana Univ. Math. J. 27(2) (1978), 331-347. [11] N. Varopoulos, Sur les ensembles de Helson, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A592-A593.

Keywords and phrases: measure preserving transformations, averaging methods, duality, topology.