Publications: D. Borwein

PAPERS IN REFEREED JOURNALS

1.    On the Cesàro summability of integrals, J. London Math. Soc 25(1950), 289-302.

2.    A summability factor theorem, J. London Math. Soc. 25(1950), 302-315.

3.    On the absolute Cesàro summability of integrals, Proc. London Math. Soc. (3)1(1951), 308-326.

4.    Note on summability factors, J. London Math. Soc. 29(1954), 198-206.

5.    Integration by parts of Cesàro summable integrals, J. London Math. Soc. 29(1954), 276-292.

6.    On the absolute summability of Stieltjes integrals, J. London Math. Soc. 29(1954), 476-486.

7.    On the abscissae of summability of a Dirichlet series, J. London Math. Soc. 30(1955), 68-71.

8.    A theorem on Riesz summability, J. London Math. Soc. 31(1956), 319-324.

9.    On a scale of Abel-type summability methods, Proc. Camb. Phil. Soc. 53(1957), 318-322.

10.    On methods of summability based on power series, Proc. Royal Soc. Edinburgh 64(1957), 342-349.

11.    A logarithmic method of summability, J. London Math. Soc. 33(1958), 212-220.

12.    On products of sequences, J. London Math. Soc. 33(1958), 352-357.

13.    Theorems on some methods of summability, Quart. J. Math. Oxford (2)9(1958), 310-316.

14.    On multiplication of (C,-µ)-summable series, J. London Math. Soc. 33(1958), 441-449.

15.    On Borel-type methods of summability, Mathematika 5(1958), 128-133.

16.    On methods of summability based on integral functions, Proc. Camb. Phil. Soc. 55(1959), 23-30.

17.    Binary and ternary transformations of sequences, Proc. Edinburgh Math.Soc. 11(1959), 175-181. (Joint paper with A.V. Boyd).

18.    On finite difference solutions of two point boundary value problems, ZAMP 10(1959), 221-232. (Joint paper with A.R. Mitchell).

19.    An extension of a theorem on the equivalence between absolute Rieszian and absolute Cesàro summability, Proc. Glasgow Math. Assoc. 4(1959), 81-83.

20.    Relations between Borel-type methods of summability, J. London Math. Soc. 35(1960), 65-70.

21.    On moment constant methods of summability, J. London Math. Soc. 35(1960), 71-77.

22.    On methods of summability based on integral functions II, Proc. Camb. Phil. Soc. 56(1960), 125-131.

23.    On strong and absolute summability, Proc. Glasgow Math. Assoc. 4(1960), 122-139.

24.    Nörlund methods of summability associated with polynomials, Proc. Edinburgh Math. Soc. 12(1960), 7-15.

25.    On Riesz summability factors, Proc. Glasgow Math. Assoc. 5(1962), 188-196. (Joint paper with B. L. R. Shawyer).

26.    On multiplication of Cesàro summable series, J. London Math. Soc. 38(1963), 393-400. (Joint paper with Y. Matsuoka).

27.    On absolute Riesz summability factors, J. London Math. Soc. 39(1964), 455-465. (Joint paper with B. L. R. Shawyer).

28.    On strong Riesz summability factors, J. London Math. Soc. 40(1965), 111-126. (Joint paper with B. L. R. Shawyer).

29.    Linear functionals connected with strong Cesàro summability, J. London Math. Soc. 40(1965), 628-634.

30.    On a class of convergent series of positive terms, J. London Math. Soc. 40(1965), 587-588.

31.    On a non-enumerable exceptional set, Amer. Math. Monthly 73(1966), 288.

32.    On a generalised Cesàro summability method of integral order, Tohoku Math. J. 18(1966), 71-73.

33.    On Borel-type methods, Tohoku Math. J. 18(1966), 283-298. (Joint paper with B. L. R. Shawyer).

34.    On a method of summability equivalent to the Cesàro method, J. London Math. Soc. 42(1967), 339-343.

35.    On Riesz and generalised Cesàro summability of arbitrary positive order, Math. Z. 99(1967), 171-177. (Joint paper with D. C. Russell).

36.    On Borel-type methods II, Tohoku Math. J. 19(1967), 232-237. (Joint paper with B. L. R. Shawyer).

37.    On generalised Cesàro summability, J. Indian Math. Soc. (Prasad Memorial Issue) 9(1967), 55-64.

38.    Strong Nörlund summability, Math. Z. 103(1968), 94-111. (Joint paper with F. P. A. Cass).

39.    Multiplication theorems for strong Nörlund summability,Math. Z. 107(1968), 33-42. (Joint paper with F. P. A. Cass).

40.    Scales of logarithmic methods of summability, Canad. Math. Bull. 12(1969), 445-452. (Joint paper with R. Phillips).

41.    A tauberian theorem for Borel-type methods of summability, Canad. J. Math. 21(1969), 740-747.

42.    A property of gradients, Amer. Math. Monthly 76(1969), 648. (Joint paper with A. Meir).

43.    On Riesz and generalised Cesàro summability, J. London Math. Soc. (2)2(1970), 61-66.

44.    On absolute Borel-type methods of summability, Proc. Amer. Math. Soc. 24(1970), 85-89.

45.    On Abel-type methods of summability, J. Reine Angew. Math. 247(1971), 139-145. (Joint paper with J. H. Rizvi).

46.    Convergence criteria for bounded sequences, Proc. Edinburgh Math. Soc. (2)19(1972), 99-103.

47.    Divergence criteria for positive series, Amer. Math. Monthly 79(1972), 1104-1106. (Joint paper with A. Meir).

48.    On strong summability, J. Reine Angew. Math. 260(1973), 119-126. (Joint paper with J. H. Rizvi).

49.    Strict inclusion between strong and ordinary methods of summability, J. Reine Angew. Math. 267(1974), 166-174. (Joint paper with F. P. A. Cass).

50.    Tauberian theorems for Borel-type methods of summability, Canad. Math. Bull. 17(1974), 167-173. (Joint paper with E. F. M. Smet).

51.    A tauberian theorem for Borel-type methods of summability, J. Reine Angew. Math. 273(1975), 153-164. (Joint paper with I. J. W. Robinson).

52.    Generalized strong summability of infinite series, J. Reine Angew. Math. 276(1975), 142-147. (Joint paper with J. H. Rizvi).

53.    Equivalence of Riesz methods of summability, J. London Math. Soc. (2)13(1976), 205-208. (Joint paper with F. P. A. Cass).

54.    A tauberian theorem for Abelian summability methods, J. Reine Angew. Math. 285(1976), 75-76. (Joint paper with B. B. Watson).

55.    On functional Cesàro and Hölder methods of summability, Canad. J. Math. 28(1976), 1058-1061. (Joint paper with B. L. R. Shawyer).

56.    Addendum to "Tauberian theorems for Borel-type methods of summability", Canad. Math. Bull. 19(1976), 245-246. (Joint paper with E. F. M. Smet).

57.    On the zeros of the power series (...) with an application to discontinuous Riesz-summability, Canad. Math. Bull. 19(1976), 417-424. (Joint paper with W. Kratz).

58.    Tauberian theorems for strong and absolute Borel-type methods of summability, Canad. Math. Bull. 20(1977), 161-172. (Joint paper with E.F. M. Smet).

59.    On certain sequences of plus and minus ones, Canad. J. Math. 30(1978), 170-179. (Joint paper with W. Gawronski).

60.    A sum of reciprocals of least common multiples, Canad. Math. Bull. 20(1978), 117-118.

61.    Tauberian theorems on a scale of Abel-type summability methods, J. Reine Angew. Math. 298(1978), 1-7. (Joint paper with B. B. Watson).

62.    Translates of sequences in sets of positive measure, Canad. Math. Bull. 21(1978), 497-498. (Joint paper with S. Z. Ditor).

63.    The Hausdorff moment problem, Canad. Math. Bull. 21(1978), 257-265; Corrections, 22(1979), 128. (Solicited paper).

64.    Matrix operators on lp, Rocky Mountain J. Math. 9(1979), 463-477. (Joint paper with A. Jakimovski).

65.    On the relation between the logarithmic and Borel-type summability methods, Canad. Math. Bull. 24(2)(1981), 153-159. (Joint paper with B. Watson).

66.    Weighted means, generalised Hausdorff matrices and the Borel property, Acta Math. Hung. 37(1981), 29-34. (Joint paper with F. P. A. Cass).

67.    Tauberian conditions for the equivalence of weighted mean and power series methods of summability, Canad. Math. Bull. 24(1981), 309-316.

68.    Matrix transformations of weakly multiplicative sequences of random variables, J. London Math. Soc. 23(1981), 363-371.

69.    Generalization of the Hausdorff moment problem, Canad. J. Math. 33(1981), 946-960. (Joint paper with A. Jakimovski).

70.    Tauberian theorems between the logarithmic and Abel-type summability methods, Pacific J. Math. 101(1982), 11-23. (Joint paper with B. Watson).

71.    On summability factors for the strong Cesàro method for integrals, Analysis 2(1982), 7-42. (Joint paper with K. Roberts).

72.    Transformations of certain sequences of random variables by generalized Hausdorff matrices, Pacific J. Math. 107,1(1983), 15-26. (Joint paper with A. Jakimovski).

73.    Generalized Hausdorff matrices as bounded operators on lp, Math. Z. 183(1983), 483-487.

74.    Nörlund matrices as bounded operators on lp, Arch. Math. 42(1984), 464-469. (Joint paper with F. Peter Cass).

75.    Conditions for inclusion between Nörlund summability methods, Acta Math. Hung. 45,1-2(1985), 151-158. (Joint paper with B. Thorpe).

76.    Convergence of lattice sums and Madelung's constant, J. Math. Phys. 26(11)(1985), 2999-3009. (Joint paper with Jonathan M. Borwein and Keith F. Taylor).

77.    On Cesàro and Abel summability factors for integrals, Canad. J. Math. 38,2(1986), 453-477. (Joint paper with B. Thorpe).

78.    On absolute generalized Hausdorff summability, Arch. Math. 46(1986), 419-427. (Joint paper with F. Peter Cass and John E. Sayre).

79.    A note on alternating series in several dimensions, The Amer. Math. Monthly 93,7(1986), 531-539. (Joint paper with J. Borwein).

80.    On generalized Hausdorff matrices, J. Approx. Theory 48,4(1986), 354-360. (Joint paper with F. Peter Cass and John E. Sayre).

81.    A Tauberian theorem concerning weighted means and power series, Math. Proc. Camb. Phil. Soc. 101(1987), 283-286. (Joint paper with A. Meir).

82.    Tauberian and other theorems concerning Dirichlet's series with non-negative coefficients, Math. Proc. Camb. Phil. Soc. 102(1987), 517-532.

83.    A Tauberian theorem concerning Borel-type and Cesàro methods of summability, Canad. J. Math. 40,1(1988), 228-247. (Joint paper with T. Markovich).

84.    On Cesàro and Borel-type summability, Proc. Amer. Math. Soc. 103,4(1988), 1108-1112. (Joint paper with T. Markovich).

85.    Enumeration of injective partial transformations, Discrete Math. 73(1989), 291-296. (Joint paper with S.A. Rankin and L.E. Renner).

86.    On strong generalized Hausdorff summability, Acta Math. Hung. 53,1-2(1989), 95-101. (Joint paper with F. Peter Cass and John E. Sayre).

87.    On relations between weighted mean and power series methods of summability, J. Math. Analysis and Applications 139,1(1989), 178-186. (Joint paper with Werner Kratz).

88.    A Tauberian theorem concerning Dirichlet series, Math. Proc. Camb. Phil. Soc. 105(1989), 481-484.

89.    Energy of static electron lattices, J. Math. Phys. 21(1988), 1519-1531. (Joint paper with J.M. Borwein, R. Shail and I.J. Zucker).

90.    Analysis of certain lattice sums, J. Math. Analysis and Applications 143,1(1989), 126-137. (Joint paper with J.M. Borwein and R. Shail).

91.    Tauberian theorems concerning Laplace transforms and Dirichlet series, Arch. Math. 53(1989), 352-362.

92.    An inclusion theorem for Dirichlet series, Canad. Math. Bull. 32(4)(1990), 479-481.

93.    Asymptotic relationships between Dirichlet series, J. Math. Analysis and Applications 147,2(1990), 604-609.

94.    Fixed point iterations for real functions, J. Math. Analysis and Applications 157,1(1991), 112-126. (Joint paper with J.M. Borwein).

95.    Weighted means and summabiltiy by the circle and other methods, J. of Approximation Theory 68,1(1992), 49-55. (Joint paper with T. Markovich).

96.    The non-local nature of the summability of Fourier series by certain absolute Riesz methods, Proc. Amer. Math. Soc. 114,1(1992), 89-94.

97.    A Tauberian theorem concerning Borel-type and Riesz summability methods, Canad. Math. Bull. 35(1)(1992), 14-20.

98.    Tauberian theorems concerning power series with non-negative coefficients, Acta Mathematica Hungarica 59,1-2(1992), 85-89.

99.    Nörlund operators on lp, Canad. Math. Bull. 36,1(1993), 8-14. [dvi file] [postscript file] [pdf file]

100.    Generalized Hausdorff and weighted mean matrices as operators on lp, J. Math. Analysis and Applications 178(1993), 517-528. (Joint paper with X. Gao). [dvi file] [postscript file] [pdf file]

101.    An O-Tauberian theorem and a high indices theorem for power series methods of summability, Math. Proc. Camb. Phil. Soc. 115(1994), 365-375. (Joint paper with W. Kratz).

102.    Weighted means and summability by generalized Nörlund and other methods, J. Math. Analysis and Applications 184(1994), 607-619. (Joint paper with R. Kiesel).

103.    Matrix operators on lp to lq, Canad. Math. Bull. 37,4(1994), 448-456. (Joint paper with X. Gao). [dvi file] [postscript file] [pdf file]

104.     Matrix transformations of power series, Proc. Amer. Math. Soc. 122,2(1994), 511-523. (Joint paper with A. Jakimovski). [dvi file] [postscript file] [pdf file]

105.    On some trigonometric and exponential lattice sums, J. Math. Analysis and Applications 188,1(1994), 209-218. (Joint paper with J.M. Borwein).

106.    On an intriguing integral and some series related to zeta(4), Proc. Amer. Math. Soc. 123(4)(1995), 1191-1198. (Joint paper with J.M. Borwein). [dvi file] [postscript file] [pdf file]

107.    Explicit evaluation of Euler sums, Proc. Edinburgh Math. Soc. 38(1995), 277-294. (Joint paper with J.M. Borwein and R. Girgensohn).

108.    Matrix transformations of series of orthogonal polynomials, Mathematika 42(1995), 427-443. (Joint paper with P. Borwein and A. Jakimovksi).

109.    Giuga's conjecture on primality, Amer. Math. Monthly 103(1)(1996), 40-50. (Joint paper with J.M. Borwein, P. Borwein, and R. Girgensohn). [dvi file] [postscript file] [pdf file]

110.    Approximate subgradients and coderivatives in Rn, Set-Valued Analysis 4(1996), 375-398. (Joint paper with J.M. Borwein and X. Wang).

111.    Convergence of Madelung-like lattice sums, Trans. Amer. Math. Soc. 350(1998), 3131-3167. (Joint paper with J.M. Borwein and C. Pinner).

112.    Simple conditions for matrices to be bounded operators on lp, Canad. Math. Bull 41(1998), 10-14.

113.    A generalization of Hardy's inequality with applications, Communications in Applied Analysis 2(1998), 309-320. (Joint paper with A. Jakimovski).

114.    A high indices Tauberian theorem, Acta. Sci. Math. (Szeged) 64(1998), 143-149. (Joint paper with W. Kratz).

115.    Matrices that commute with certain Hausdorff matrices, Analysis 18(1998), 227-244. (Joint paper with A. Jakimovski). [dvi file] [postscript file] [pdf file]

116.    Two Tauberian theorems for Dirichlet series methods of summability, Acta. Sci. Math. (Szeged) 65(1999), 139-168. (Joint paper with J. Beurer and W. Kratz).

117.    Weighted mean operators on lp, Canad. Math. Bull 43(2000), 406-412. [dvi file] [postscript file] [pdf file]

118.    Surprize maximization, Amer. Math. Monthly 107(2000),517-527. (Joint paper with J.M. Borwein and P. Maréchal). [dvi file] [postscript file] [pdf file]

119.    Some remarkable properties of sinc and related integrals, Ramanujan J. 5(2001), 73-89. (Joint paper with J.M. Borwein). [dvi file] [postscript file] [pdf file]

120.    One-sided Tauberian theorems for Dirichlet series methods of summability, Rocky Mountain J. Math. 31(2001), 797-830. (Joint paper with W. Kratz and U. Stadtmüller). [dvi file] [postscript file] [pdf file]

121.    Refined convexity and special cases of the Blaschke-Santalo inequality, Math. Inequalities and Applications 4(2001), 631-638. (Joint paper with J.M. Borwein, G. Fee, and R. Girgensohn).

122.    Multi-variable sinc integrals and volumes of polyhedra, Ramanujan J. 6(2002), 189-208. (Joint paper with J.M. Borwein and B.A. Mares Jr.). [dvi file] [postscript file] [pdf file]

123.    A one-sided Tauberian theorem for the Borel summability method, J. Math. Analysis and Applications 293(2004), 285-292. (Joint paper with W. Kratz ). [pdf file]

124.    Finding and excluding $b$-ary Machin-type individual digit formulae, Can. J. Math. 56(2004), 897-925. (Joint paper with J.M. Borwein and W.F. Galway ). [pdf file]

125.    Weighted convolution operators on $\ell_p$, Canad. Math. Bull. 48(2005), 175-179. (Joint paper with W. Kratz ). [pdf file]

126.    Parametric Euler sum identities, J. Math. Analysis and Applications 316(2006), 328-338. (Joint paper with D.M. Bradley and J.M. Borwein). [pdf file]

127.    On the dynamics of certain recurrence relations, Ramanujan J. 13(2007), 63-101.(Joint paper with J.M. Borwein, R. Crandall and R. Mayer ). [pdf file]

128.    Van der Pol expansions of L-series, Canad. Math. Bull. 50(2007), 11-23. (Joint paper with J.M. Borwein ). [pdf file]

129.    Hypergeometric forms for Ising-class integrals, Experiment. Math. 16(2007), 257-276. (Joint paper with D.H. Bailey, J.M. Borwein and R.E. Crandall ). [pdf file]

130.     The evaluation of Bessel functions via exp-arc integrals, J. Math. Analysis and Applications 341(2008), 888-901. (Joint paper with J.M. Borwein and O-Y. Chan ). [pdf file]

131.     Effective Laguerre asymptotics, SIAM J. Numer. Anal. 46(2008), 3285-3312.(Joint paper with J.M. Borwein and R.E. Crandall ). [pdf file]

132.     Surprising sinc sums and integrals, Amer. Math. Monthly 115(2008), 888-901. (Joint paper with J.M. Borwein and R. Baillie ). [pdf file]

133.     $L_p$-norms and the sinc function, Amer. Math. Monthly 117(2010), 528-539. (Joint paper with J.M. Borwein and I.E. Leonard ). [pdf file]

PAPERS IN REFEREED CONFERENCE PROCEEDINGS

134.    Generalization of the Hausdorff moment problem, Nonlinear Analysis and Applications, Proceedings of International Conference on Nonlinear Analysis and Applications, St. John's, Newfoundland, (1981), 33-37. (Joint paper with A. Jakimovski).

135.    The non-local nature of the summability of Fourier series by certain absolute Riesz methods, Israel Mathematical Conference Proceedings 4(1991), 69-72.

OTHER PUBLICATION

The ultrastructure of monkey foveal photoreceptors, with special reference to the structure, shape, size, and spacing of the foveal cones, The Amer. J. of Anatomy 159(1980), 125-146. (Joint paper with B. Borwein, J. Medeiros, and J. McGowan).

PUBLISHED INVITED BOOK REVIEWS

i.    A miscellany for mathematicians and others, CMS Notes September (2001), 3-4. Review of Mathematical conversations. Selections from the Mathematical Intelligencer compiled by Robin Wilson and Jeremy Gray.

ii.    Meandering in Euler's neighbourhood, CMS Notes November (2004), 6-7. Review of Gamma, exploring Euler's constant by Julian Havel.

iii.   Review in Bull Amer. Math. Soc.42(2005), 401-406, of Tauberian theory, A century of developments by Jacob Korevaar.

PAPER SUBMITTED TO A REFEREED JOURNAL

Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant. (Joint paper with J.M. Borwein, M.L. Glasser and J.G Wan)

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Last update: December 01, 2010