Roger Jones

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Roger Jones is an American mathematician.

He has his Ph.D. in mathematics from Rutgers University and has recently retired from a professorship in mathematics at DePaul University in Chicago. There he taught everything from remedial math to graduate-level courses. During his tenure at DePaul, Roger published numerous research papers in math, was awarded an excellence in teaching award, chaired the DePaul University Math Department, and was awarded National Science Foundation grants related to teaching mathematics. He has also worked with the Chicago Public Schools on improving math instruction.

Roger was honored for his work in Harmonic analysis and Ergodic theory at the International Conference on Harmonic Analysis and Ergodic theory that was held in the name of Roger and his colleague Marshall Ash. Information about that conference can be viewed here: Conference on Harmonic Analysis and Ergodic Theory

Roger has since retired from teaching at DePaul and moved to Northern Wisconsin, where he teaches mathematics at Conserve School.

1 Appointments
2 Book
3 Articles
4 Professional Memberships
5 Course syllabi

[edit] Appointments

• 1974-1977: DePaul University, Assistant Professor

• 1977-1984: DePaul University, Associate Professor

• 1982-1985: DePaul University, Chairman: Department of Mathematics

• 1984-2004: DePaul University, Professor

• 2004-present: DePaul University, Professor Emeritus

[edit] Book

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

[edit] Articles

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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),111-219.

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 d0exponentiells, (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,(Coauthor: 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 averages, (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) 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 Lp, (Co-author: J. Olsen), Israel Journal of Math. 77 (1992) 33-54.

19. Subsequence ergodic theorems for Lp contractions, (Co-authors: J. Olsen, M. Wierdl) Trans. A.M.S. 351 (1992) 837-850.

20. Ergodic averages on spheres, J. d0Analysis 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., (1996) 16 267-305.

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, 1966 229–247. (Papers in these proceedings were refereed.)

31. Integer and fractional parts of good averaging sequences in ergodic theory, (Coauthors:Michael Boshernitzan, Mate Wierdl) Convergence in Ergodic Theory and Probability, Edited by Bergelson, March, and Rosenblatt, Walter de Gruyter & Co., Berlin, 1966 117–132. (Papers in these proceedings were refereed.)

32. A Banach principle for L1, (Co-author: Alexandra Bellow), Advances in Mathematics, 120 (1996) 155–172.

33. The strong sweeping out property for lacunary sequences, Riemann sums, convolution 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 (Coauthors: 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. Ergodic theory and connections with analysis and probability New York J. of Math., 3A (1997) 31-67.

37. Variation in probability, ergodic theory and analysis (Co-authors: P. Schwartz, M. Akcoglu). Il. J. of Math., 42 (1998) 154-177.

38. 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.

39. Approximation of L2 Processes by Gaussian Processes (joint with M. Akcoglu, J. Baxter and M.D. Ha), New York J. of Mathematics, 4 (1998) 75-82.

40. Oscillation in ergodic theory, (Co-authors: R. Kaufman, J. Rosenblatt, M. Wierdl), Ergodic Theory and Dyn. Sys., 18 (1998) 889-935.

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. Strong sweeping out for block sequences and related ergodic averages (Co-author: M. Akcoglu), Illinois J. of Mathematics, 43 (1999) 447-456.

43. Counting in ergodic theory (Co-authors: J. Rosenblatt and M. Wierdl), Canadian J. of Math., 51 (1999) 996-1019.

44. An exponential estimate for convolution powers, Studia Mathematica, 137 (1999) 195-202.

45. Oscillation and variation for the Hilbert transform (Co-authors: J. Campbell, K. Reinhold, M. Wierdl) Duke Journal of Mathematics, 105 (2000) 59-83.

46. Reverse inequalities (Co-author: J. Rosenblatt) Journal of Fourier Analysis and Applications, 3 (2000) 325-341.

47. Lp norm local estimates for exponential sums, (Coauthors: B. Anderson, J. M. Ash, D. G. Rider, B. Saffari) Comptes Rendus de l’Academie des Sciences, 330(2000), 765-769.

48. Oscillation inequalities for rectangles (joint with J. Rosenblatt and M. Wierdl), P.A.M.S., 129 (2001) 1349-1358.

49. The worst sums in ergodic theory, (joint with M. Akcoglu, J. Rosenblatt and M. Wierdl), Michigan Math. J. 47 (2000), no. 2, 265–285. .4

50. Differential and ergodic transforms, (joint with J. Rosenblatt), Math. Ann., 323 (2002) 525-546.

51. On Restricted weak type (1,1), (joint with M. Akcoglu, J. Baxter and A. Bellow), Israel J. Math., 124 (2001) 285-297. View Article

52. Oscillation in ergodic theory: higher dimensional results (Co-authors: J. Rosenblatt and M. Wierdl) Israel J. Math. 135 (2003), 1–27.

53. Oscillation and variational inequalities for convolution powers (joint work with K. Reinhold), Ergodic Theory and Dyn. Sys., 21 (2001) 1809-1829.

54. Strong sweeping out for convolution powers, (joint with M. Akcoglu, and J. Rosenblatt), preprint 10 pages.

55. Oscillation and variation for singular integrals in higher dimensions (Co-authors: J. Campbell, K. Reinhold, M. Wierdl) Trans. Amer. Math. Soc. 355 (2003), no.5, 2115–2137.

56. Exponential sums with coefficients 0 or 1 and concentrated Lp norms, in progress, 22 pages. (Coauthors: B. Anderson, J. M. Ash, D. G. Rider, B. Saffari)

57. Variation inequalities for the Fejer and Poisson Kernels, (Co-author: G. Wang) Trans. Amer. Math. Soc. 356 (2004), no. 11, 4493–4518. View Article

58. SLLN for weighted independently identically distributed random variables, (Coauthors: J. Baxter, M. Lin, J. Olsen), J. Theoret. Probab. 17 (2004), no. 1, 165–181.

59. On the uniqueness of the ergodic maximal function. Proc. Amer. Math. Soc. 132 (2004), no. 4, 1087–1090. View Article

60. On restricted weak type (1, 1): the continuous case, (Co-author: Paul A. Hagelstein, Proc. Amer. Math. Soc.Proc. Amer. Math. Soc. 133 (2005), no. 1, 185–190

61. Strong sweeping out for lacunary sequences Chapel Hill Ergodic Theory Workshops, 137–144, Contemp. Math., 356, Amer. Math. Soc., Providence, RI, 2004.

62. Besicovitch weights and the necessity of duality restrictions in the weighted ergodic theorem (Co-author: Ciprian Demeter) Chapel Hill Ergodic Theory Workshops, 127–135, Contemp. Math., 356, Amer. Math. Soc., Providence, RI, 2004. View Article

63. On strong laws of large numbers with rates (Co-authors: Guy Cohen and Michael Lin) Chapel Hill Ergodic Theory Workshops, 101–126, Contemp. Math., 356, Amer. Math. Soc., Providence, RI, 2004.