Bruce A Watson

Research Publications

1. A. Kalauch, W. Kuo, B.A. Watson, A Hahn-Jordan decomposition and Riesz-Frechet representation theorem in Riesz spaces.

2. Y. Azouzi, M.A. Ben Amor, J. Homann, M. Masmoudi, B.A. Watson, The Kac formula and Poincare recurrence theorem in Riesz spaces. Proceedings of the American Mathematical Society, Series B, in press.

3. M.A. Ben Amor, J. Homann, W. Kuo, B.A. Watson, Characterization of conditional weak mixing via ergodicity of the tensor product in Riesz spaces. Journal of Mathematical Analysis and Applications, 524 (2023), no. 127074, pp. 1-12.

4. C. Bartels, S. Currie, B.A. Watson, Sturm-Liouville problems with transfer conditions Herglotz dependent on the eigenparameter: eigenvalue asymptotics. Complex Analysis and Operator Theory, 15 (2021), no. 71, pp. 1-29.

5. J.M. Homann, W.-C. Kuo, B.A. Watson, Ergodocity in Riesz spaces. In Kikianty, E., Mabula, M., Messerschmidt, M., van der Walt, J.H., Wortel, M. (eds.) Positivity and its Applications. Trends in Mathematics. Birkhauser, 2021.

6. J.M. Homann, W.-C. Kuo, B.A. Watson, On the Koopman-von Neumann convergence condition of Cesaro means in Riesz spaces. Proceedings of the American Mathematical Society, Series B, 8 (2021), 75-85.

7. N. Mushambi, B.A. Watson, B. Zinsou, Generalization of the theorems of Barndorff-Nielsen and Balakrishnan-Stepanov to Riesz spaces. Positivity, 24 (2020), 753-760.

8. W.-C. Kuo, D. Rodda, B.A. Watson, The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces. Journal of Mathematical Analysis and Applications, 481 (2020), 123462.

9. W.-C. Kuo, D. Rodda, B.A. Watson, Strong sequential completeness of the natural domain of a conditional expectation operator in Riesz spaces. Proceedings of the American Mathematical Society, 147 (2019), 1597-1603.

10. W.-C. Kuo, M.J. Rogans, B.A. Watson, Near Epoch dependence in Riesz spaces. Journal of Mathematical Analysis and Applications, 467 (2018), 462-479.

11. S. Currie, T.T. Roth, B.A. Watson, Eigenvalue interlacing for first order differential systems with periodic 2x2 matrix potentials and quasiperiodic boundary conditions. Operators and Matrices, 12 (2018), 489-499.

12. C.A. Bartels, S. Currie, M. Nowaczyk, B.A. Watson, Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter - Hilbert space formulation. Integral Equations and Operator Theory, 90:34 (2018), 1-20.

13. S. Currie, M. Nowaczyk, B.A. Watson, Inverse problems with a general transfer condition. Operator Theory: Themes and Variations, TSAM20, (2018) 129-143.

14. R. Picard, B.A. Watson, On boundary damped inhomogeneous Timoshenko beams and related problems. Mathematical Methods in the Applied Sciences, 41 (2018), 1054-1061.

15. W.-C. Kuo, M.J. Rogans, B.A. Watson, Mixing inequalities in Riesz spaces. Journal of Mathematical Analysis and Applications, 456 (2017), 992-1004.

16. S. Currie, T.T. Roth, B.A. Watson, Borg's periodicity theorems for first order self-adjoint systems with complex potentials. Proceedings of the Edinburgh Mathematical Society, 2017 (60), 615-633.

17. R. Picard, B.A. Watson, On boundary damped inhomogeneous Timoshenko beams. Proc. Appl. Math. Mech., 16 (2016), 877-878.

18. P.A. Binding, P.J. Browne, B.A. Watson, Weighted p-Laplacian problems on a half-line. Journal of Differential Equations, 2016 (260) 1372-1391.

19. W.-C. Kuo, J. Vardy, B.A. Watson, Bernoulli Processes in Riesz spaces. Operator Theory: Advances and Applications, Order structures and Applications, Springer-Verlag, 263-274, 2016

20. Y. Azouzi, W.-C. Kuo, K. Ramdane, B.A. Watson, Convergence in Riesz spaces with conditional expectation operators. Positivity, 2015 (19), 647-657.

21. S. Currie, M. Nowaczyk, B.A. Watson, Inverse scattering on the line with a transfer condition. Mediterranean Journal of Mathematics, 2015 (12), 729-750.

22. S. Currie, T. Roth, B.A. Watson, First-order systems in C2 on R with periodic matrix potentials and vanishing instability intervals. Mathematical Methods in the Applied Sciences, 2015 (38), 4435-4447.

23. J. Vardy, B.A. Watson, On the decompositions of T-quasi-martingales on Riesz spaces. Positivity, 18 (2014), 425-437.

24. R. Picard, B.A. Watson, Evolutionary problems involving Sturm-Liouville operators. Operator Theory: Advances and Applications, 236 (2013/2014), 393-406.

25. S. Currie, M. Nowaczyk, B.A. Watson, Forward scattering on the line with a transfer condition. Boundary Value Problems, 2013(2013), no.255, 1-14.

26. P.A. Binding, P.J. Browne, B.A. Watson, Eigencurves of non-definite Sturm-Liouville problems for the p-Laplacian, Journal of Differential Equations, 255 (2013), 2751-2777.

27. W.-C. Kuo, J.J. Vardy, B.A. Watson, Mixingales on Riesz Spaces. Journal of Mathematical Analysis and Applications, 402 (2013), 731-738.

28. S. Currie, B.A. Watson, Quadratic eigenvalue problems for second order systems. Complex Analysis and Operator Theory, 6 (2012), 729-748.

29. J.J. Vardy, B.A. Watson, Markov Processes on Riesz Spaces. Positivity, 16 (2012), 373-391.

30. S. Currie, B.A. Watson, Indefinite Boundary Value Problems on Graphs. Operators and Matrices, 5 (2011), 565-584.

31. P.A. Binding, P.J. Browne, B.A. Watson, Non-definite Sturm-Liouville problems for the p-Laplacian, Operators and Matrices, 5 (2011), 649-664.

32. C.C.A. Labuschagne, B.A. Watson, Discrete stochastic integration in Riesz spaces. Positivity, 14 (2010), 859-875.

33. M. Korostenski, C.C.A. Labuschagne, B.A. Watson, Reverse martingales in Riesz spaces. Operator Theory, Advances and Applications. 195 (2010), 213-230.

34. P.A. Binding, P.J. Browne, B.A. Watson, Darboux transformations and the factorization of generalized Sturm-Liouville problems. Proceedings of the Royal Society of Edinburgh. 140 A (2010), 1-29.

35. P.A. Binding, B.A. Watson, An inverse nodal problem for two-parameter Sturm-Liouville systems, Inverse Problems, 25 (2009), 085005 (19pp).

36. S. Currie, B.A. Watson, The M-matrix inverse problem for the Sturm-Liouville equations on graphs, Proceedings of the Royal Society of Edinburgh, Section A 139 (2009), 775-796.

37. B.A. Watson, An Ando-Douglas type theorem in Riesz spaces with a conditional expectation operators, Positivity,13 (2009), 543-558.

38. P.J. Browne, B.A. Watson, Oscillation theory for a quadratic eigenvalue problem, Quaestiones Mathematicae, 31 (2009), 345-357.

39. S. Currie, B.A. Watson, Green’s functions and the regularised traces of Sturm−Liouville operators on graphs, Proceedings of the Edinburgh Mathematical Society, 51 (2008), 315-335.

40. S. Currie, B.A. Watson, M−matrix asymptotics for Sturm−Liouville problems on graphs, J. Computational and Applied Mathematics, 218 (2008), 568−578.

41. Faierman, M. Moller, B.A. Watson, Completeness theorems for a non−standard two−parameter eigenvalue problem , Integral Equations and Operator Theory, 60 (2008), 37−52.

42. W.−C. Kuo, C.C.A. Labuschagne, B.A. Watson, Amarts on Riesz Spaces, Acta Mathematica Sinica (English Series), 24 (2008), 329−342.

43. S. Currie, B.A. Watson, Boundary estimates for solutions of non−homogeneous boundary value problems on graphs, 12th WSEAS International Conference on Applied Mathematics, Cairo, Egypt, December 29−31, 2007, pp. 37−42.

44. S. Currie, B.A. Watson, Inverse nodal problems for Sturm−Liouville equations on graphs, Inverse Problems, 23 (2007) 2029−2040.

45. W.−C. Kuo, C.C.A. Labuschagne, B.A. Watson, Ergodic Theory and the Law of Large Numbers on Riesz Spaces, J. Mathematical Analysis and Applications, 325 (2007), 422−437.

46. S. Cullender, W.−C. Kuo, C.C.A. Labuschagne, B.A. Watson, Measure−free martingales with applications to classical martingales, in Soft Methods for Integrated Uncertainty Modelling, Springer, Berlin, 2006. Advances in Soft Computing, Springer Verlag, 2006, pp. 121−128.

47. P.A. Binding, P.J.Browne, B.A. Watson, Sturm−Liouville problems with reducible boundary conditions, Proceedings of the Edinburgh Mathematical Society, 49 (2006), 593− 608.

48. W.−C. Kuo, C.C.A. Labuschagne, B.A. Watson, Convergence of Riesz Space Martingales, Indagationes Mathematicae, 17 (2006), 271−283.

49. S. Currie, B.A. Watson, Dirichlet−Neumann Bracketing for Boundary Value Problems on Graphs, Electronic Journal of Differential Equations, 2005 (2005) No 93, 1−11.

50. W.−C. Kuo, C.C.A. Labuschagne, B.A. Watson, A Zero−One Law for Riesz Space and Fuzzy Processes, IFSA2005, Beijing, Springer Verlag, 2005, pp. 393−397.

51. W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Conditional expectation operators on Riesz spaces. Journal of Mathematical Analysis and Applications, 303 (2005), 509-521.

52. S. Currie, B.A. Watson, Eigenvalue asymptotics for differential operators on graphs, Journal of Computational and Applied Mathematics, 182 (2005), 13-31.

53. P.A. Binding, P.J. Browne, W. Code, B.A. Watson, Transformation of Sturm−Liouville Problems with Decreasing Affine Boundary Conditions, Proceedings of the Edinburgh Mathematical Society, 47 (2004), 533−552.

54. P.A. Binding, P.J. Browne, B.A. Watson, Recovery of the m-function from spectral data for generalised Sturm-Liouville problems, Journal of Computational and Applied Mathematics, 171 (2004), 73-91.

55. W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Riesz space and fuzzy upcrossing theorems, Proceedings of SMPS2004, Springer Verlag, 2004, pp. 101-108. Corrected proof.

56. W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indagationes Mathematicae, N.S., 15 (2004) 435-451.

57. P.A. Binding, P.J. Browne, B.A. Watson, Equivalence of inverse Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, Journal of Mathematical Analysis and Applications, 291 (2004), 246-261.

58. P.A. Binding, P.J. Browne, B.A. Watson, Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, II, Journal of Computational and Applied Mathematics, 148 (2002), 147-168.

59. P.A. Binding, P.J. Browne, B.A. Watson, Decomposition of spectral asymptotics Sturm-Liouville equations with a turning point, Advances in Differential Equations, 8 (2003), 491-511.

60. P.A. Binding, P.J. Browne, B.A. Watson, Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, I, Proceedings of the Edinburgh Mathematical Society, 45 (2002), 631-645.

61. P.A. Binding, P.J. Browne, B.A. Watson, Spectral asymptotics for Sturm-Liouville equations with indefinite weight, Transactions of the American Mathematical Society, 354 (2002), 4043-4065.

62. P.A. Binding, P.J. Browne, B.A. Watson, Inverse spectral problems for left-definite Sturm-Liouville equations with indefinite weight, Journal of Mathematical Analysis and Applications, 271 (2002), 383-408.

63. P.A. Binding, P.J. Browne, B.A. Watson, Spectral isomorphisms between generalized Sturm-Liouville problems, Operator Theory: Advances and Applications, 130 (2001), 135-152.

64. P.A. Binding, P.J. Browne, B.A. Watson, Transformations between Sturm-Liouville problems with eigenparameter dependent and independent boundary conditions, Bulletin of the London Mathematical Society, 33 (2001), 749-757.

65. P.A. Binding, P.J. Browne, B.A. Watson, Spectral problems for non-linear Sturm-Liouville equations with eigenparameter dependent boundary conditions, Canadian Journal of Mathematics, 52 (2000), 248-264.

66. P.A. Binding, P.J. Browne, B.A. Watson, Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions, Journal of the London Mathematical Society, 62 (2000), 161-182.

67. B.A. Watson, Inverse spectral problems for weighted Dirac systems, Inverse Problems, 15 (1999), 793-805.

68. S.D. Travlos, B.A. Watson, Time - the forgotten dimension: a new method for the solution of time-dependent Schroedinger equations Suid-Afrikaanse Tydskrift van Chemistry, 48 (1995), 44-47.

Works in progress

Our book on Stochastic Processes in Riesz spaces, which I work on when I find time.

Upcoming conferences

We (organizers: Kuo, Ter Horst, Watson and Zinsou) will be hosting FAOTSA23 at the Wits Rural Facility from 3 July 2023 until 7 July 2023.