Preprints

1999

      • An Integral Operator with Applications, (with R.S. Chisholm and W.N. Everitt), J. Inequalities and Applications, 3, 1999, 245-266. PDF.
      • H.J.S. Smith and the Fermat two squares theorem, (with F. Clarke, W.N. Everitt, and S.J.R. Vorster), The American Mathematical Monthly, 106(7), 1999, 652-665. PDF.

2000

      • The left-definite spectral theory for the classical Hermite differential equation, (with W.N. Everitt and R. Wellman), J. Comput. Appl. Math., 121, 2000, 313-330. PDF.

2001

      • Orthogonal polynomial eigenfunctions of second order partial differential equations, (with K.H. Kwon and J.K. Lee), Trans. Amer. Math. Soc., 353(9), 2001, 3629-3647. PDF.
      • Orthogonal polynomial solutions to spectral type differential equations: Magnus’ conjecture, (with K.H. Kwon and G.J. Yoon), J. Approximation Theory, 112, 189-215, 2001. PDF.
      • Orthogonal polynomial solutions of linear ordinary differential equations, (with W.N. Everitt, K.H. Kwon, and R. Wellman), J. Comput. Appl. Math., 133(2001), 85-109. PDF.
      • Self-adjoint operators generated from non-Lagrangian symmetric differential equations having orthogonal polynomial solutions, (with W.N. Everitt, K.H. Kwon, J.K. Lee, and S.C. Williams), Rocky Mountain J. Math., 31(3), 899-937, 2001.PDF.

2002

      • A general left-definite theory for certain self-adjoint operators with applications to differential equations, (with R. Wellman), J. Differential Equations, 181, 280-339, 2002. PDF.
      • On the right-definite and left-definite spectral theory of the Legendre polynomials, (with J. Arvesú and F. Marcellán), J. Comput. Anal. and Appl., 4(4), 363-387, 2002. PDF.
      • On properties of the Legendre differential expression (with W. N. Everitt and V. Maric), Result. Math. 42, 42-68, 2002. PDF.
      • Legendre polynomials, Legendre-Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression, (with W. N. Everitt and R. Wellman), J. Comput. Appl. Math., 148, 213-238, 2002. PDF.

2004

      • Orthogonal polynomials satisfying partial differential equations belonging to the basic class, (with J. K. Lee), J. Korean Math. Soc. 41(2004), No. 6, 1049-1070.PDF
      • The fourth-order Bessel-type differential equation, (with J. Das, W. N. Everitt, D. B. Hinton, and C. Markett), Applicable Analysis, 83(4) (2004), 325-362. PDF
      • On Analytic Sampling Theory (with A. G. Garcia), J. Comput. Appl. Math., 171 (2004), 235-246. PDF.
      • The Sobolev orthogonality and spectral analysis of the Laguerre polynomials for positive integers k, (with W. N. Everitt and R. Wellman), J. Comput. Appl. Math., 171(2004), 199-234. PDF.

2005

      • Additional spectral properties of the fourth-order Bessel-type differential equation(with W. N. Everitt, H. Kalf, and C. Markett), Math. Nachr., 278, 12-13, (2005), 1538-1549. PDF.

2006

      • A construction of real weight functions for certain orthogonal polynomials in two variables (with J. K. Lee), J. Math. Anal. Appl. 319(2006), no. 2, 475-493. PDF.
      • Sobolev orthogonal polynomials in two variables and second-order partial differential equations, (with J. K. Lee), J. Math. Anal. Appl., 322(2006), no. 2, 1001-1017. PDF
      • Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions, (with K. H. Kwon and G. J. Yoon), J. Math. Anal. Appl., 324(2006), 285-303. PDF
      • The fourth-order Bessel equation: eigenpackets and a generalized Hankel transform (with W. N. Everitt, H. Kalf, and C. Markett), Integral Transforms Spec. Funct. 17(2006), no. 12, 845-862. PDF

2007

      • Left-definite variations of the classical Fourier expansion theorem, (with A. Zettl),Electron. Trans. Numer. Anal., 27 (2007), 124-139. PDF
      • Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression, (with W. N. Everitt, K. H. Kwon, R. Wellman, and G. J. Yoon), J. Comput. Appl. Math., 208(2007), 29-56. PDF
      • Some remarks on classical Lagrangian symmetric differential expressions and their composite powers (with W. N. Everitt and D.Tuncer), Adv. Dyn. Syst. Appl.2(2), 2007, 187-206. PDF

2008

      • Left-definite theory with applications to orthogonal polynomials, (with A. Bruder, D. Tuncer, and R. Wellman), J. Comput. Appl. Math., 233(2010), 1380-1398. PDF
      • A combinatorial interpretation of the Legendre-Stirling numbers, (with G. E. Andrews), Proc. Amer. Math. Soc., 137 (2009), 2581-2590. PDF
      • Quasi-separation of the biharmonic partial differential equation (with W. N. Everitt, B. T. Johannson, and C. Markett), IMA (Oxford) J. Appl Math. 2009 74(5), pp. 685-709 . PDF
      • Ghost matrices and a characterization of symmetric Sobolev bilinear forms, (with K. H. Kwon and G. J. Yoon), Linear Algebra Appl., 431 (2009) 104-119. PDF
      • Properties of the solutions of the fourth-order Bessel-type differential equation, (with W. N. Everitt and C. Markett), J. Math. Anal. Appl., 359 (2009), 252-264.PDF

2009

      • Variation of parameters and solutions of composite products of linear differential equations, (with J. L. López), J. Math. Anal. Appl., 369(2010), 658-670. PDF
      • The Legendre-Stirling Numbers, (with G. E. Andrews and W. Gawronski), Discrete Math., 311(2011), 1255-1272. PDF

2010

      • Factorization of second-order linear differential equations and Liouville-Neumann expansions, (with E. García, J. L. López, and E. Pérez Sinusía), Mathematical and Computer Modelling, 57 (2013), 1514-1530. PDF
      • Non-classical Jacobi polynomials and Sobolev orthogonality, (with A. Bruder),Results Math., 61(2012), no. 3-4, 283-313. PDF

2011

      • On the spectra of left-definite operators, (with R. Wellman), Complex Analy. Oper. Theory, 7(2) (2013), 437-455. PDF
      • The Legendre equation and its self-adjoint operators, (with A. Zettl), Electron. J. Diff. Equ., Vol. 2011, No. 69, pp. 1-33.PDF
      • The Jacobi-Stirling Numbers, (with G. E. Andews, E. Egge, W. Gawronski), J. Combinatorial Theory Ser. A, 120(2013), 288-303. PDF

2012

      • Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters α = β = -1 “, (with A. Bruder), Ann. Mat. Pura Appl., DOI 10.1007/s10231-012-0284-8. PDF

2013

    • The Spectral Theory of the X1 – Laguerre Polynomials, (with M. J. Atia and J. Stewart), Advances in Dynamical Systems and Applications, to appear. PDF