Almost Everywhere Convergence II. Proceedings of the by Alexanra Bellow, Alexandra Bellow, Roger L. Jones

By Alexanra Bellow, Alexandra Bellow, Roger L. Jones

Virtually all over Convergence II comprises chosen papers shape the second one foreign convention on nearly in every single place convergence in likelihood and Ergodic idea, which came about on October 16-20, 1989 at Northwestern collage. It comprises survey papers and significant unique contributions and will entice researchers within the zone of ergodic conception and harmonic research in addition to to graduate scholars getting into those fields of research

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A. P. Calderon, Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sei. A. 59 (1968), 349-353. 7. L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135-157. 8. M. Cotlar, A unified theory of Hubert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105-167. 9. H. Davenport and H. Halberstam, The values of a trigonometrical polynomial at well spaced points, Mathematika 13 (1966), 91-96. 10. C. Fefferman, On the convergence of multiple Fourier series, Bull.

If v is the velocity of the particle, its position in Ω at time t is τίνω. Let Ω = Ω x [0,oo), and let μ = μ ® λ be the product of μ and the Lebesgue measure A. ,v)p(dw)A(dv) = JJf(r_„,a,,v)l H (u,,v)d,«lA. The convergence of this quantity for t — ► oo follows by applying the following theorem of Hopf to the flow with reversed time. The visit of this author at the University of Göttingen was supported by & Humbolt prize. This research was also partially supported by NSF grant DMS-8910947. This work was completed during a visit of the second author at the School of Mathematics of the Georgia Institute of Technolgoy.

Soc. , 1987. 39 18. K. Petersen, Another proof of the existence of the ergodic Hubert transform, Proc. Amer. Math. Soc. 88 (1983), 39-43. 19. H. , 1989. Department of Mathematics CB#3250, Phillips Hall University of North Carolina Chapel Hill, NC 27599 USA 40 On Hopfs Ergodic Theorem for Particles with Different Velocities by 1 Alexandra Bellow and Ulrich Krengel2 Summary In 1936 E. Hopf [H2] answered a limiting problem on the distribution of a cloud of particles in a box with the help of a general L r mean ergodic theorem.

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