WILLIAM R. WADE

email: William.wade@biola.edu

CV:

EDUCATION

A.B. cum laude, M.A., Ph.D. University of California, Riverside

HONORS

Fulbright to Moscow University in Russia

Fulbright to the Indian Statistical Institute in Bangalore

Several National Science Foundation grants

An international conference held in his honor in Eger, Hungary, 2003

Eisenhower grants and the National Science Foundation grants (via the Appalachian Math and Science Consortium

Three Graduate Student Association awards for outstanding teaching at the graduate level

A National Alumni Teaching Award for undergraduate teaching

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