VITA - January, 2001
Roger L. Jones

EDUCATION

ACADEMIC APPOINTMENTS:

ADMINISTRATIVE APPOINTMENTS:

PUBLICATIONS:

  1. The ergodic maximal function with cancellation, Ann. of Prob., 4 (1976), 91-97.
  2. Inequalities for the ergodic maximal function, Studia Mathematica, 60 (1977), 111-129.
  3. Singular integral operators with complex homogeneity, (Co-authors: J.M. Ash, P.F. Ash, C.L. Fefferman), Studia Mathematica, 65 (1979), 31-50.
  4. An analog of the Marcinkiewicz integral in ergodic theory, Studia Mathematica, 68 (1981), 281-289.
  5. Optimal numerical differentiation using three function evaluations, (Co-author: J.M. Ash), Mathematics of Computation, 37 (1981), 159-167.
  6. New proofs for the maximal ergodic theorem and the Hardy-Littlewood maximal theorem, Proc. A.M.S., 87 (1983), 681-684.
  7. Inegalites sur des sommes d'exponentiells,(Co-authors: J.M. Ash, B. Saffari), C. R. Acad. Sc. Paris, 296 (1983) 899-902.
  8. Ornstein's L log L Theorem, Proc. A.M.S., 91 (1984), 262-264.
  9. Optimal numerical differentiation using n function evaluations, (Co-authors: J.M. Ash, Svante Janson) Estratto da Calcolo, 21 (1984), 151-169.
  10. Convergence of series conjugate to a convergent multiple trigonometric series},(Co-author: J. M. Ash) Bulletin Des Sciences Math\'ematiques, 110 (1986), 177-224.
  11. Necessary and sufficient conditions for a maximal ergodic theorem along subsequences, Ergodic Theory and Dynamical Systems Journal, 7 (1987), 203-210.
  12. The mean value theorem for generalized derivatives, (Co-author: J. M. Ash) Proc. A.M.S., 101 (1987), 263-271.
  13. Maximal inequalities for pairs of ergodic transformations, Radovi Matematicki, 4 (1988), 55-61.
  14. Convergence for moving average, (Co-author: A. Bellow, J. Rosenblatt) Ergodic Theory and Dynamical Systems, 10 (1990) 43 -62.
  15. Almost everywhere convergence of weighted averages, (Co-authors: A.Bellow, J. Rosenblatt) Math. Ann. 293 (1992) 399-426.
  16. Harmonic analysis and ergodic theory, (Co-authors: A. Bellow, J. Rosenblatt) in Almost Everywhere Convergence, Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, June 11-14, 1988. G. Edgar and L. Sucheston ed. Academic Press, 1989, pp. 73-98. (Papers in these proceedings were refereed.)
  17. Almost everywhere convergence of powers, (Co-authors: A. Bellow, J. Rosenblatt) in Almost Everywhere Convergence, Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, June 11-14, 1988. G. Edgar and L. Sucheston ed. Academic Press, 1989, pp. 99-120. (Papers in these proceedings were refereed.)
  18. Subsequence pointwise ergodic theorems for operators in L^p, (Co-author: J. Olsen), Israel Journal of Math. 77 (1992) 33-54.
  19. Subsequence ergodic theorems for L^p contractions, (Co-authors: J. Olsen, M. Wierdl) Trans. A.M.S. 351 (1992) 837-850.
  20. Ergodic averages on spheres, J. d'Analysis Math., 61 (1993) 29-45.
  21. Multi--parameter moving averages, (Co- author: J. Olsen) in Almost Everywhere Convergence II, Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory II, A. Bellow and R. Jones ed., Academic Press, (1991) 127-149. (Papers in these proceedings were refereed.)
  22. A remark on singular integrals with complex homogeneity, Proc. A.M.S. 114 (1992) 763-768.
  23. Divergence of averages obtained by sampling a flow, (Co-authors: M. Akcoglu, A. del Junco, and A. Bellow) Proc. A. M. S. 118 (1993) 499-505.
  24. Almost everywhere convergence of convolution powers, (Co-authors: A. Bellow, J. Rosenblatt) Erogdic Theory and Dynamical Systems, 14 (1994) 415-432.
  25. Convergence and divergence of ergodic averages, (Co- author: M. Wierdl), in Ergodic Theory and Dynamical Systems, 14 (1994) 515-535.
  26. Ergodic theorems for convolutions of a measure on a group, (Co-authors: J. Rosenblatt, A. Tempelman), Illinois J.of Math., 38 (1994) 521-553.
  27. Multiparameter weighted ergodic theorems for operators, (Co-author: J. Olsen), Canadian Journal, 46 (1994) 343-356.
  28. Divergence of sequences of operators, (Co-authors: M. Akcoglu and D. Ha) in Topological vector spaces, algebras and related areas, A. T. Lau and I. Twedddle editors, Pitman Research Notes in Mathematics, Longman Scientific and Technical, New York (1994) 175-192.(Papers in these proceedings were refereed.)
  29. Square functions in ergodic theory, (Co-authors: J. Rosenblatt, Iosif Ostrovskii), Ergod. Th. & Dynam. Sys., 16 (1996) 267-305.
  30. Convergence of ergodic averages, (Co-author: Mate Wierdl) Convergence in Ergodic Theory and Probability, Edited by Bergelson, March, and Rosenblatt, Walter de Gruyter \& Co., Berlin, 1996 229--247. (Papers in these proceedings were refereed.)
  31. Integer and fractional parts of good averaging sequences in ergodic theory, (Co-authors: Michael Boshernitzan, Mate Wierdl) Convergence in Ergodic Theory and Probability, Edited by Bergelson, March, and Rosenblatt, Walter de Gruyter \& Co., Berlin, 1996 117--132. (Papers in these proceedings were refereed.)
  32. A Banach principle for , Co-author: Alexandra Bellow), Advances in Mathematics, 120 (1996) 155--172.
  33. The strong sweeping out property for lacunary sequences, Riemann sums, convolutin powers, and related matters}, (Co-authors: M. Akcoglu, A. Bellow, V. Losert, K. Reinhold, and M. Wierdl) Ergodic Theory and Dyn. Sys., 16 (1996) 207-253.
  34. On approach regions for conjugate Poisson integrals and singular integrals, (Co-authors: S. Ferrando, K. Reinhold) Studia Math. 120 (1996) 169-182.
  35. Sweeping out properties for operator sequences, (joint with M. Akcoglu and M. D. Ha), Canadian Journal of Math., 49 (1997) 3-23.
  36. Gaussian Distribution measures, (joint with M. Akcoglu, J. Baxter and M.D. Ha) , New York J. of Math., 4 (1998) 75-82.
  37. Oscillation in ergodic theory, (Co-authors: R. Kaufman, J. Rosenblatt, M. Wierdl),  Ergodic Theory and Dyn. Sys., 18 (1998) 889-935.
  38. Variation in probability, ergodic theory and analysis, (Co-authors: P. Schwartz, M. Akcoglu), Il  J. of Math, 42 (1998) 154-177.
  39. Ergodic theory and connections with analysis and probability, New York J. of Math., 3A (1997) 31-67.
  40. Weighted subsequence ergodic theorems along sequences of density zero, (joint with M. Lin and J. Olsen), New York J. of Mathematics, 3A  (1998) 89-98.
  41. Integer sequences with big gaps and the pointwise ergodic theorem, (Co-authors: M. Lacey and M. Wierdl) Ergodic Theory and Dyn. Sys, 19 (1999) 1295-1308.
  42. Oscillation and variation for the Hilbert transform, (Co-author:  J. Campbell, K. Reinhold and M. Wierdl) Duke Math. J.,. 105 (2000) 59-83.
  43. Oscillation inequalities in ergodic theory: Higher dimensional results, (Co-authors: J. Rosenblatt and M. Wierdl) preprint - 21 pages, submitted for publication.
  44. Counting in ergodic theory, (Co-authors: J. Rosenblatt and M. Wierdl) Canadian J. of Math., 51 (1999) 996-1019.
  45. Reverse inequalities, (Co-author: J. Rosenblatt) , J. Fourier Analysis and Applications, 6 (2000) 325-341.
  46. Strong sweeping out for block sequences and related ergodic averages,  Illinois J. of Mathematics. 43 (1999) 447-456.  (Co-author: M. Akcoglu)
  47. Differential and ergodic transforms, (Co-author: J. Rosenblatt), preprint 20 pages, submitted for publication.
  48. Divergence of convolution powers, (Co-authors: M. Akcoglu, A. Bellow, J. Rosenblatt), preprint 10 pages.
  49. An exponential estimate for convolution powers, Studia Mathematica, 137 (1999) 195-202.
  50. The worst sums in ergodic theory, (Co-authors:  M. Akcogou and  J. Rosenblatt) preprint: 20 pages, to appear in Michigan Math J.
  51. Oscillation inequalities for convolution operators, (Co-author:  K. Reinhold) preprint -- 29 pages, to appear in Ergodic Theory and Dyn. Sys.
  52. Lp norm local estimates for exponential sums, (Co-authors: B. Anderson, J. M. Ash, D. Rider, and B. Saffari) C. R. Acad. Sci Paris, 330 (2000) 765-769.
  53. Oscillation inequalities for rectangles, (Joint with J. Rosenblatt and M. Wierdl) To appear in Proc. A.M.S.
  54. On restricted weak type (1,1), the discrete case, (Joint with M. Akcoglu, J. Baxter and A. Bellow) to appear in Israel Journal of Math.

BOOKS:

Editor (with A. Bellow) of : Almost everywhere convergence, Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory II, Octiber 14-18, 1989, Academic Press, 1991.

SEMINARS and CONFERENCES:

  1. Organized a conference on Harmonic Analysis and Probability which was held at DePaul in July, 1986. This conference was supported by a grant from the National Science Foundation and the Conference Board on Mathematical Sciences. The conference attracted about 30 mathematicians from across the nation.
  2. Organized (with A. Bellow) a conference on Almost everywhere convergence in probability and ergodic theory, Northwestern University, October 1989. This conference was supported by the National Science Foundation, National Security Agency, Mathematics Institute, and Northwestern University. The conference had 50 talks, with speakers from 7 countries including the U.S.S.R.
  3. Organized a special session on ``Ergodic Theory'' at the A.M.S. meeting held at DePaul im March 1995.
  4. Organized (with Mark Pinsky and Joseph Rosenblatt) a conference in honor of Alexandra Bellow. This conference was held at Northwestern in October, 1997.

MEMBERSHIP IN PROFESSIONAL ORGANIZATIONS:

  1. Mathematical Association of America
  2. American Mathematical Society

GRANTS and AWARDS:

  1. A grant from the National Science foundation to organize and run a CBMS Lecture series. The conference was held in July, 1986
  2. Two small grants from the University research council, the quality of instruction council, and two grants from the Liberal Arts committee on Researchand Development.
  3. (With A. Bellow) A two year grant from the National Science Foundation for summer support, and running a conference at Northwestern University. 1989-1990.
  4. (With A. Bellow) A two year grant from the National Science Foundation for summer support. 1991-1992.
  5. (With Lynn Narasimhan) A three year grant with UIC towork on the CPMP program. DePaul's part of the grant isabout $200,000. This is a program to work with Chicago area teachers to try to improve high school mathematics education.
  6. A three year grant from the National Science Foundationfor summer support. 1993-1995.
  7. A university award for Excellence in Teaching. I received this award in 1995. Only three awards are made each year in LA& S.
  8. Summer grant for the summer 1996 from the Liberal Arts and Sciences Reserarch and Development committee. Title: Oscillation in ergodic theory. (This grant was returned to the college, since I subsequently received a larger grant from the National Science Foundation.
  9. A two year grant from the National Science Foundation for summer support. 1996-1997.
  10. A summer grant for the summer 1998 from the Liberal Arts and Sciences Reserarch and Development committee. Title: Ergodic Theory via Martingales.
  11. A grant (joint with Mark Pinsky of Northwestern) to support a conference that was held October 23-26, 1997. This conference was held in honor of Alexanda Bellow.