NAME:  William R. Wade

DATE AND PLACE OF BIRTH:  October, 28, 1943, Los Angeles, California

EMPLOYMENT:

2012-present,    Chair, Math and Computer Science Department, Biola University, La Mirada, California
1978-2011,       Professor, University of Tennessee
1994-2003,       Professor and Associate Head, University of  Tennessee
1972-1978,       Associate Professor, University of Tennessee
1968-1972,       Assistant Professor, University of Tennessee
6/1968-8/1968, Computer Analyst, Aerospace Corp. (SBO)
1966-1968,       NDEA Fellow
1965-1966,       Grad. Teaching Assistant, Univ. of California (Riverside)
 

CONSULTING WORK:

 December, 1970 - August, 1976, Oak Ridge National Laboratory
 June, 1969 - November, 1970, Gaseous Diffusion Plant, Oak Ridge

PUBLICATIONS:

1.  William R. Wade, "A uniqueness theorem for Haar and Walsh series," Trans. Amer. Math. Soc., Vol. 141: 187-194, 1969.

2.  _____, "Uniqueness theory for Cesaro summable Haar series," Duke Math. J., Vol. 38:         211-227, 1971.

3. _____, "Summing closed U-sets for Walsh series," Proc.   Amer. Math. Soc., Vol. 29: 123-125, 1971.

4.  _____, "Uniqueness of Haar series which are  (C, 1) summable to Denjoy integrable functions," Trans. Amer.   Math. Soc., Vol. 176: 489-498, 1973.

5.  _____, "The bounded convergence theorem," Amer. Math. Monthly, Vol. 81: 387-389, 1974.

6.  _____, "Haar and Walsh series of Perron integrable functions," J. Ind. Math. Soc., Vol. 38, 19-35, 1974.

7.  _____, "Sets of uniqueness and   -capacity on the Group 2 ," Trans. Amer. Math. Soc., Vol. 208: 309-315, 1975.

8.  _____, "Growth of Haar series on dyadic rationals,"  Proc. Amer. Math. Soc., Vol. 50: 198-201, 1975.

9. _____, "Growth conditions and uniqueness of Walsh series," Mich. Math. J., Vol. 24:   153-155, 1977.

10.  _____, "Sets of uniqueness for Haar series," Acta Math. Acad. Sci. Hung., Vol. 30: 265-281, 1977.

11. ____ and David C. Harris,  "Sets of divergence on the group  2 ," Trans. Amer. Soc., Vol. 240: 385-392, 1978.

 12.  _____, "H(n)-sets for the group of integers of a  p-series field," Proceedings of Symposia in Pure Mathematics, Vol. 35: 325-327, 1979.

13. _____, "Sets of uniqueness for the group of integers of p-series field," Canadian J. of Math., Vol. 31: 858-866, 1979.

14.  _____, and V.A. Skvorcov, "Generalizations of some results concerning Walsh series and the dyadic derivative," Anal. Math., Vol. 5: 249-255, 1979.

15. _____, "Walsh series and growth of functions on nested dyadic intervals," Journal Ind. Math. Soc., Vol. 43: 1-11, 1979.

16.  _____, and G.E. Lippman, "Pseudofunctions and  uniqueness on the group of integers of a p-series field," Acta. Math. Acad. Sci. Hung., Vol. 35: 1-12, 1980.

17.  _____, "Uniqueness of Walsh series which satisfy an average growth condition," SIAM Journal of Mathematical  Analysis, Vol. 11: 933-977, 1980.

18.  _____, and C.H. Powell, "Term by term dyadic differentiation," Canad. J. of Math., Vol. 33: 247-256,  1981.

19. _____, "Applications of uniqueness for Walsh series to sampling theory," 4. Aachener Kolloquium, "Theory and Applications of Signal Processing: 64-68, 1981.

20.  _____, "Locally constant dyadic derivatives," Per.   Math. Hungar., Vol. 13: 71-74, 1982.

21.  _____, and K. Yoneda, "Uniqueness and quasi-measures on the group of integers of a p-series field," Proc. Amer. Math. Soc., Vol. 84: 202-206, 1982.

22.  _____, "Recent developments in the theory of Walsh  series," Internat. J. Math. Vol. 5, No. 4, 625-673,     1982.

23.  _____, "Lp inequalities for Walsh series, 0<p<1",   Acta. Sci. Mat., Vol. 46: 233-241, 1983.

24.  _____, "Walsh-Fourier coefficients and locally constant  functions," Proc. Amer. Math. Soc., Vol. 87(3):  434-438, 1983.

25.  _____, "Decay of Walsh series and dyadic differentiation," Trans. Amer. Math. Soc., Vol. 277(1): 413-420, 1983.

26.  _____, "A Growth Estimate for Cesaro partial sums of  multiple Walsh-Fourier series", Colloq. Math. Soc. Janos Bolyai, Vol. 49: 975-991, 1985.

27. _____, "Recent developments in the theory of Haar series," Colloquium Mathematicum, Vol. 52: 213-238,  1986.

28.  _____, "A Unified Approach to Uniqueness of Walsh   Series and Haar Series," Proc. Amer. Math. Soc., Vol. 99: 61-65, 1987.

29. _____, and F. Schipp, "A Fundamental Theorem of Dyadic Calculus for the Unit Square", Applicable Analysis Vol. 34: 203-218, 1989.

30.  _____, F. Moritz and F. Schipp, "On the Integrability   of Double Walsh series with Special Coefficients", Michigan Math. J. Vol. 37:191-201, 1990.

 31. _____, The Gibbs derivative and term by term differentiation of Walsh series, "Theory and Applications of Gibbs Derivatives", P. L. Butzer and R. S. Stankovic, Editors, Math. Inst. Belgrad (1990), 59-72.

  32.  _____, and C.H. Powell, Term by Term Dyadic   Differentiation of Rapidly Convergent Walsh series, J. Approx. Theory and Appl. Vol 7: 20-40, 1991.

 33. _____, F. Schipp, and P. Simon, "Walsh Series:  An Introduction to Dyadic Harmonic Analysis", A. Hilgar Publishing Ltd. (Institute of Physics), Bristol and New York, 1990 [A 561 page research monograph, comprehensive in scope, full of new ideas and better methods than available before in the literature]

34. _____, F. Moritz and F. Schipp, "Cesaro Summability of Double Walsh-Fourier Series,"  Trans. Amer. Math. Soc., Vol 329: 131-140, 1992.

35. _____, Review of "Walsh Series and Transforms", Bull. Amer. Math. Soc., Vol. 26: 348-359, 1992.

36. _____, (with F. Schipp), "Norm Convergence and Summability of Fourier Series with respect to Certain Product Systems", Approximation Theory, Vol. 138: 437-452, Marcel Dekker, Inc., 1992.

37. _____, (with G.E. Albert) "Haar Systems for Compact Geometries" Acta Math. Hung. Vol 61: 21 - 41, 1993.

38. _____, (with C. Powell), "Paley Sets and Term by Term Dyadic Differentiation of Walsh Series" Acta Math. Hung. Vol 62: 89-96, 1993.

39. _____, Vilenkin-Fourier series and approximation, Colloq. Math. Soc. J. Bolyai Vol 58: 699-734, 1994.

40. _____, (with S. Fridli), Rate of convergence and dyadic differentiability of Walsh series, J. D Anal. Math. Vol 62: 287-305, 1994.

41. _____, "An introduction To Analysis," 565 pp., Prentice Hall, 1995.

42. _____, A Walsh System for Polar Coordinates, Computers Math. Applic., Vol 30:221-227, 1995.

 43. _____, (with J. Tateoka), "On Strong Approximation and Summability by Cesaro Means on Besov Spaces over the 2-series field," Acta Sci. Math. Sci. (Szeged), Vol 60: 685-703, 1995.

 44. _____, (with F. Schipp), "Transforms on Normed Fields,"  Janus Pannon. Univ. Pecs,1-175, 1995.

45. _____, "Harmonic Analysis on Vilenkin Groups,"Fourier Analysis and approximation, N.A.I. Publ: 339-370, 1996

46. _____, Dyadic Harmonic Analysis, Contemporary Math.,  Vol 208: 313-350, 1997.

47. _____,Walsh functions and Walsh series, Encyclopedia of  Mathematics, Suppl. I, Kluwer Publishing Co., p. 484 1997.

48. _____, (with F. Schipp), "Fast Fourier Transforms on Binary Fields," Approx. Theory and Appl. Vol. 14 (1998), 91-100.

49. _____, Growth of Cesaro means of double Vilenkin-Fourier series of unbounded type. Fourier Analysis, Birkhauser Basel, 41-50, 1999.

50.  _____, Summability estimates of double Vilenkin-Fourier Series, Math. Pannon. Vol 10, 67-75, 1999.

51.  _____, (with S. Perrin), Sets of uniqueness for Vilenkin groups, Acta. Sci. Math. (Szeged) Vol. 66: 631-644, 1999.

52. _____, (with F. Schipp), Zak Transforms on binary fields, Journal Approx. Theory Vol 101: 182-195, 1999.

53.   _____, An Introduction to Analysis, 2nd Ed. Prentice Hall, 2000.

54.  _____, (with P.W. Wade), Recursions which produce Pythagorean triples, College Math. J. Vol 31: 98-101, 2000.

55.  _____, (with F. Schipp), Mellin transforms on Binary fields Applied and Computational Harmonic Anal. Vol 9: 54-71, 2001.

56.  _____, (with F. Moricz), An analogue of a theorem of F. Lukacs for double Walsh series, Acta Math. Hung. Vol 95: 323-336, 2002.

57. _____, Sets of uniqueness for martingale subsequences of Vilenkin series, Colloq. Math. Soc. J. Bolyai: 433-441, 2002.

58. _____, A Tauberian theorem for Vilenkin Series, Proc. Amer. Math. Soc., Vol. 131: 2877-2881, 2003.

59. _____, (with D. Daniel), Uniqueness of Cesaro summable double Walsh series, Anal. Math. Vol. 30: 33-46, 2004.

60. _____, An Introduction to Analysis, 3rd Ed. Prentice Hall, 2004.

61. _____, Uniqueness of almost everywhere convergent Vilenkin series, Canadian Math. Bull., Vol. 47, 475-480, 2004.

62. _____, Review of "Mathematical Analysis", SIAM Review, Vol. 46, 766-770, 2005

63. ______"Uniqueness of Square Summable Walsh Series," Acta. Sci. Math. (Szeged), Vol 72: 147-157, 2006.

64. ______"A Dialogue Between Calculator and Algebra," Math Teacher (NCTM), Vol 99:391-393, 2006.

65. _____, (with F. Moricz), On the Problem of Uniqueness of the Trigonometric Moment constants, Acta Math. Hungar. Vol 111, 313-324, 2007.

66. _____, An Introduction to Analysis, 4th ed, Prentice Hall, 2009

67. _____, Convergence of Filtered Walsh-Fourier Series, Annales Univ. Sci. Budapest., Sect. Comp. Vol 33, 365-375, 2010

68. _____, (with C. Powell), "A Partial Ordering that Generates Filtered Walsh Series", Acta Math.Hung. Vol 140, 162-168, 2013.

69. ____, Term by Term Dyadic Differentiation of Walsh Series, Chapter 9, in "Dyadic Walsh Analysis Since 1924," Atlantis Press, Paris, 2015, pp 347-358.

last updated: November 2015
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