Publications

Thesis

Integralgleichungen mit variablen Grenzen für spezielle Funktionen der mathematischen Physik, 86 pages, Konstanz, May 1979.

Book and two book chapters

Multiparameter eigenvalue problems and expansion theorems, Lecture Notes in Mathematics 1356, 157 pages, Springer, New York Heidelberg Berlin 1988. (MR 90d,47021)

Chapter on Spheroidal Wave Functions for the NIST Handbook of Mathematical Functions, Cambridge University Press, 2010. (dlmf.nist.gov) (MR2655370)

Chapter on Lamé Functions for the NIST Handbook of Mathematical Functions, Cambridge University Press, 2010. (dlmf.nist.gov) (MR2655369)

Journal articles published

Integralgleichungen mit variablen Grenzen für spezielle Funktionen der mathematischen Physik, J. Reine Angew. Math. 319, 118-132 (1980). (MR 82d,33017)

On multiparameter theory, J. Math. Anal. Appl. 86, 44-53 (1982).(MR 83g,47018)

with Hans Weber, A unified treatment of vector integration, Comment. Math. Univ. Sanct Pauli 31, 33-48 (1982). (MR 84g,28011)

Integral relations for Lamé functions, SIAM J. Math. Anal. 13, 978-987 (1982). (MR 84b,33010)

Integralgleichungen für periodische Lösungen HillscherDifferentialgleichungen,Analysis 3, 189-203 (1983). (MR 85h,34035)

with Hans Weber, Der Wertebereich atomloser Inhalte, Arch. Math. 40, 464-474 (1983). (MR 84k,28005)

On the completeness of eigenvectors of right definite multiparameterproblems,Proc. Roy. Soc. Edinburgh 96A, 69-78 (1984).(MR 86a,47014)

Integral representations for products of Lam&eacute functions by use offundamental solutions,SIAM J. Math. Anal. 15, 559-569 (1984).(MR 85d,33026)

with Hans Weber, A new approach to integral representations of linearoperators, Bolletino U.M.I. (6) 3-B, 171-197 (1984).(MR 85f,47036)

with R. Schäfke, A note on the paper “Existence conditionsfor eigenvalue problems generated by compact multiparameter operators”by P. Binding, P. J.Browne and L. Turyn, Proc. Roy. Soc. Edinburgh 101A, 147-148 (1985). (MR 87h,47046)

with P. Binding, Existence and uniqueness of indexed multiparametriceigenvalues, J. Math. Anal. Appl. 116, 131-146 (1986).(MR 88a,47021)

with R. Schäfke, On the reduction of the Poincare rankof singular systems of ordinary differential equations,J. Reine Angew. Math. 365, 80-96 (1986). (MR 87g,34010)

On the minimal eigenvalue of a positive definite operator determinant, Proc. Roy. Soc. Edinburgh 103A, 201-208 (1986).(MR 88b,15021)

On an expansion theorem of F. V. Atkinson and P. Binding, SIAM J. Math. Anal. 18, 1669-1680 (1987).(MR 89d,47032)

with Hans Weber, Nonlinear transformations on spaces of continuousfunctions, Studia Math. 86, 221-237 (1988).(MR 89d,47146)

with R. Schäfke, Bounds for the eigenfunctions ofmultiparameter Sturm-Liouville systems, Asymptotic Analysis 2, 139-159 (1989). (MR 91d,34088)

with R. Schäfke, On the formal fundamental solution of adifferential equation depending on a parameter, Funkc. Ekvac. 33, 1-17 (1990). (MR 92f,34005)

The expansion of a holomorphic function in a Laplace series, SIAM J. Math. Anal. 21, 771-781 (1990). (MR 91f,33005)

On the regularity of wavelets, IEEE Trans. Information Theory 38, 872-876 (1992). (MR 93f,42058)

with R. Schäfke, Asymptotic analysis of the equichordal problem, J. Reine Angew. Math. 425, 9-60 (1992). (MR 93d,52003)

with G. Walter, Wavelets based on orthogonal basic splines, Applic. Analysis 47, 71-86 (1992). (MR 96c,41021)

with P. Binding, On a problem of R. G. D. Richardson, Proc. Edinburgh Math. Soc. 35, 337-348 (1992). (MR 93k,34181)

with P. Binding, On the geometry of degree conditions inmultiparameter oscillation theorems, J. Diff. Integral Equations 6, 277-290 (1993). (MR 93m,34036)

The expansion of a holomorphic function in a series of Lamé products, J. Approx. Theory 75, 167-174 (1993). (MR 95c,32002)

On the differential equation y”+exp(y^m-t)=0,Asymptotic Analysis 10, 63-75 (1995). (MR 95m,34024)

Asymptotic regularity of compactly supported wavelets, SIAM J. Math. Anal. 26, 1075-1087 (1995). (MR 96h,42031)

Frames of wavelets in Hardy Space,Analysis 15, 405-421 (1995). (MR 97b,42061)

with Hong-Tae Shim, On the Gibbs phenomenon for wavelet expansions, J. Approx. Theory 84, 74-95 (1996). (MR 97j,42019)

Asymptotic spectrum of multiparameter eigenvalue problems, Proc. Edinburgh Math. Soc. 39, 119-132 (1996).(MR 97b,47015)

with P. Binding, Eigencurves for two-parameter Sturm-Liouvilleequations, SIAM Rev. 38, 27-48 (1996). (MR 97f,34015)

Quadratic growth of convergence radii for eigenvalues of two-paramterSturm-Liouville equations, J. Differential Equations 128, 327-345 (1996). (MR 97d,34025)

Sturm-Liouville problems with indefinite weights and Everitt’s inequality,Proc. Roy. Soc. Edinburgh 126A, 1097-1112 (1996). (MR 98a,34096)

with R.E. Svetic, On the ultimate Peano derivative, J. Math. Anal. Appl. 218, 439-452 (1998). (MR 99b,26006)

Expansions of analytic functions in spherical harmonics,Complex Variables 35, 213-224 (1998).(MR 99b,33026)

On the growth of convergence radii for the eigenvalues of the Mathieuequation, Math. Nachr. 192, 239-253 (1998).(MR 2000a,34053)

with N. Bansai, G.G. Hamedani, E. Key, H. Zhang, J. Behboodian,Some characterizations of the normal distribution, Statist. Probab. Lett. 42 (1999), 393-400. (MR 2000h,62013)

Extending Peano derivatives, necessary and sufficient conditions,Fund. Math. 159, 219-229 (1999).(MR 2000b,26009)

Asymptotics of convergence radii for the two-parameter Airy equation,Dynamics of Continuous, Discrete and Impulsive Systems 5, 31-38 (1999).(MR 2000a,34054)

with P. Binding, A spectrum determined by eigencurves, Math. Nachr. 202, 5-15 (1999). (MR 2000c,47093)

Expansion in products of Heine-Stieltjes polynomials,Constr. Approx. 15, 467-480 (1999).(MR 2000i,33017)

Convexity of the Lyapunov exponent, Linear Algebra Appl. 294, 35-48 (1999).(MR 2001d,82018)

Eigenvalue problems for Bessel’s equation and zero-pairs of Besselfunctions, Studia Sci. Math. Hung. 35, 261-280 (1999).(MR 2001g,33012)

with R. Swanson, Invariants of weak equivalence in primitive matrices,Ergodic Theory Dynam. Systems 20, 611-626 (2000).(MR 2001h,37034)

Convergence radii for eigenvalues of two-parameter Sturm-Liouville problems, Analysis 20, 225-236 (2000).(MR 2002a,34034)

with R. Svetic, The minimal Denjoy index of symmetric perfect sets,Real Analysis Exchange 25, 329-342 (1999/2000). (MR 2001c,26001)

with X. He, Riesz bases of solutions of Sturm-Liouville equations,J. Fourier Anal. Appl. 7 (2001), 297-307. (MR 2002b,42046)

with G. G. Hamedani, Certain characterizations of normaldistribution via transformations, J. Multivariate Anal. 77 (2001), 286-294. (MR 2002e,62008)

with P. Binding, Existence of asymptotics of eigenvalues ofindefinite systems of Sturm-Liouville and Dirac type, J.Differential Equations 172 (2001), 116-133. (MR 2002d,34152)

with R. Svetic, The Denjoy index and symmetric perfect sets,Ital. J. Pure Appl. Math. 9 (2001), 153-164. (MR 2002f,26002)

with X. He and E. Key, Perturbation of orthonormal bases inL²-spaces, Integral Equations Operator Theorey 41 (2001),396-409. (MR 2002g,42041)
On some conjectures of Askey, Asymptot. Anal. 27 (2001), 321-334. (MR 2003k,33030)

with P. Binding, Oscillation theory for Sturm-Liouville problemswith indefinite coefficients, Proc. Roy. Soc. Edinburgh Sect. A 131, 989-1002. (MR 2003b,34066)

with G. G. Hamedani, A characterization of symmetric random variables,Communications in Statistics 32 (2003), 723-728. (MR 2004b,62030)

The coexistence problem for periodic solutions of the Ince equation,Analysis 23 (2003), 97-105. (MR 2004c,34074)

with P. Binding, Right semidefinite generalized eigenvalue problems,Proc. Edinburgh Math. Soc. 46 (2003), 561-573.(MR 2004j,47036)

Error estimates for the Rayleigh-Ritz approximations of eigenvalues and eigenfunctionsof the Mathieu and spheroidal wave equation, Constr. Approx. 20 (2004), 39-54.(MR 2004m,33031)

Matrix Riccati equations and matrix Sturm-Liouville problems, J. Differential Equations 197 (2004), 26-44.(MR 2005h,34017)

with G. G. Hamedani and E. Key, Solution to a functional equation and its application to stable and semi-stable-type distributions, Statist. Prob. Lett. 69 (2004), 1-9.(MR 2005f,39070)

On Riemann surfaces of analytic eigenvalue functions,Complex Variables 49 (2004), 169-182.(MR 2004m,34061)

Four remarks on the eigenvalues of Lamé’s equation, Anal. Appl. (Singap.) 2 (2004), 161-175.(MR 2005e,33017)

with E. Key, Eigenvalue multiplicities of products of companion matrices,The Electronic Journal of Linear Algebra 11 (2004), 103-114.(MR 2111517)

with P. Binding, Prüfer angle asymptotics for Atkinson’s semidefinite Sturm-Liouville Problem,Math. Nachr. 278 (2005), 1458-1475.(MR 2006e,34192)

with G.G. Hamedani, Certain characterizations of the uniform distribution, Metrika 61 (2005), 117-125.(MR 2006e,62022)

Eigenvalue problems of Atkinson, Feller and Krein, and their mutual relationship,Electron. J. Differential Equations 48 (2005), 1-15.(MR 2005k,34103)

with P. Binding, Interlacing and oscillation for Sturm-Liouville problems withseparated and coupled boundary conditions,J. Comput. Appl. Math. 194 (2006), 75-93. (MR 2007a,34050)

Eigenvalues associated with Borel sets, Real Anal. Exchange 31 (2005/06), 111-124. (MR 2006m,34061)

Instability intervals for the Hill and Ince equation,Analysis (Munich) 25 (2005), 189-204. (MR 2007b,34063)

Generalized ellipsoidal and sphero-conal harmonics,SIGMA Symmetry Integrability Geom. Methods Appl. 2 (2006), Paper 071, 16 pp. (electronic).(MR 2007i,35034)

with G.G. Hamedani, An inverse problem for a class ofcontinuous distributions with skewness, Statist. Probab. Lett. 76 (2006), 945-951.(MR 2008e,60032)
The coexistence problem for the Heun equation, Math. Nachr. 279 (2006), 1823-1834.(MR 2008c,34184)

with A. Zettl, Inverse spectral theory for Sturm-Liouville problems with finite spectrum,Proc. Amer. Math. Soc. 135 (2007), 1129-1132. (MR 2007f,34017)
with H. Shim and G. Walter, Gibbs’ Phenomenon In Higher Dimensions,J. Approx. Theory 145 (2007), 20-32. (MR 2008b,41016)

with P. Binding, A generalized eigenvalue problem in the max algebra,Linear Algebra Appl. 422 (2007), 360-371. (MR 2008c,15014)

with P. Binding, Inverse oscillation theory for Sturm-Liouville problemswith non-separated boundary conditions, Inverse Problems 23 (2007), 343-355. (MR 2008a,34018)

with G.G. Hamedani and J. Weselowski, Characterization problemsrelated to the Shepp property, Commun. Stat. 36 (2007), 1049-1058. (MR2396529)

with G.G. Hamedani, Characterizations of continuous symmetric distributions based onfamilies of skewed distributions, Commun. Stat. 36 (2007), 2329-2338. (MR2398058)

Approximation of eigenvalues of some differential equations by zeros oforthogonal polynomials, J. Comput. Appl. Math. 218 (2008), 488-500. (MR2392572)
Factorial series connected with the Lambert function, anda problem posed by Ramanujan, Ramanujan J. 16 (2008), 235-245. (MR2429899)

with J. Blimke, J. Myklebust, S. Merrill, Four-shell ellipsoidal model employing multipole expansionin ellipsoidal coordinates, Medical & Biological Engineering & Computing 46 (2008), 859-869.

with V. Larsen, An idealized model of the one-dimensional carbon dioxide rectifier effect, Tellus 60 (2008), 525-536.

with G.G. Hamedani, A short note on certain characterizations of the power function distribution,J. Stat. Theory Appl. 7 (2008), 137-140. (MR2424585)

External ellipsoidal harmonics for the Dunkl-Laplacian, SIGMA Symmetry Integrability Geom. Methods Appl. 4(2008), Paper 091, 13 pp.(MR2470505)

with G.G. Hamedani, Oscillation of nth order forced functional differential equations,Journal of Appl. Math. Stat. and Informatics 4 (2008), 213-218.

with A. Clough, G.G. Hamedani, G. Krenz and A. Manuel, Complete monotonicity of flow and cross-sectional sampledtransport functions for rigid right tubular tubes, J. Math. Anal. Appl. 352 (2009), 702-710.(MR2501914)

with Q. Kong and A. Zettl,Matrix representations of Sturm-Liouville problems with finite spectrum,Results Math. 54 (2009), 103-116. (MR2529630)

with G.G. Hamedani, Letter to the editor, The American Statistician 63 (2009), 295.

with G.G. Hamedani, Oscillation of a Class of Higher Order Forced Functional Differential Equations, II,Journal of Appl. Math. Stat. and Informatics 5 (2009), 45-50.

with M. Chugunova, Spectral analysis of an operator arising in fluid dynamics,Studies in Applied Mathematics 123 (2009), 291-309. (MR2561711)

with M. Chugunova,Study of a differential operator arising in fluid dynamics, Operators and Matrices 3 (2009), 525-540. (MR2597678)

Asymptotic expansion of L²-norms ofsolutions to the heat and dissipative wave equations, Asymptotical Analysis 67 (2010), 85-100. (MR2643372)

with P. Binding, Bounds for eigenvalues of the p-Laplacian with weight function of bounded variation, in Topics in Operator Theory, Volume 2, Systems and Math. Physics (2010), 99-114. (MR2683237)

On the canonical density of the half-Cauchy distribution,J. Stat. Theory Appl. 9 (2010), 325-336. (MR2809944)

with N. Ebrahimi, G.G. Hamedani and E. Soofi,A class of models for uncorrelated random variables.J. Multivariate Anal. 101 (2010), 1859-1871. (MR2651961)

with G.G. Hamedani,On distributions of order statistics and their applications to uniform distribution.Metrika 74 (2011), 287-295. (MR2822162)

with G.G. Hamedani, On the distribution of certain spacings, Communications in Statistics-Theory and Methods 40 (2011), 510-514. (MR2765844)

with A. Milani,Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations.Appl. Math. 56 (2011), 425-457. (MR2852065)

with K. Helmes and R. Stockbridge, Analysis of production decisions under budget restrictions,Stochastics 83 (2011), 583-609. (MR2842597)

with G.G. Hamedani and J. Behboodian,A note on sub-independent random variables and a class of bivariate mixtures.Studia Sci. Math. Hungarica 49 (2012), 19-25.

with P. Binding, A Prüfer angle approach to the periodic Sturm-Liouville problem.Amer. Math. Monthly 119 (2012), 477-484.

with P. Binding, A non-standard multiparameter Sturm-Liouville eigenvalue problem,Proceedings of the Royal Soc. Edinburgh 142A (2012), 673-690.

with Runhuan Feng, Modeling Credit Value Adjustment With Downgrade-Triggered Termination Clause.Insurance, Mathematics and Economics 51 (2012), 409-421.

with Runhuan Feng, Analytical calculation of risk measures for variable annuity guarantee benefits,Insurance, Mathematics and Economics 51 (2012), 626-648.

with H. S. Cohl,Definite integrals using orthogonality and integral transforms, SIGMA 8 (2012), 077, 10 pages.

with H. S. Cohl,Eigenfunction expansions for a fundamental solution of Laplace’s equation on R³ in parabolic and elliptic cylinder coordinates.J. Phys. A, Math. Theor.\ 45 (2012), 355204.

with G.G.Hamedani,Some remarks on Arslan’s 2011 paper.Journal of Computational and Applied Mathematics 237 (2013), 1-4.

with Dexuan Xie, A modified nonlocal electrostatic model for protein in water and its analytical solutions for ionic Born models.Commun. Comput. Phys. 13 (2013), 174-194.

with J. Michel, On the spectral surface of a model two-parameter Sturm-Liouville problem,Complex Variables and Elliptic Equations 58 (2013), 333-350.

J. Behboodian, N. Bansal, G.G. Hamedani, The Pitman inequality for exchangeable random vectors, Stat. Prob. Letters 83, (2013),1825-1829.

with P. Binding, A Prüfer angle approach to semidefinite Sturm-Liouville problems with coupling boundary conditions,J. Differential Equations, published online May 15, 2013.

with H. Cohl and C. MacKenzie, Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals,J. Math. Anal. Appl. 407 (2013), 211-225.

with H. Cohl, Separation of variables in an asymmetric cyclidic coordinate system, J. Math. Phys., published online June 2013.

with J. Wood, A note on the asymptotic expansion of generalized hypergeometric functions,to appear in Analysis and Application.

Contributions to conference proceedings

Continuous extension of operators and the representation theorem of Riesz,Proceedings of the conference on vector measures and integral representation of operators, and on functional analysis, Banach space geometry, Essen 1982, Vorlesungen Fachbereich Mathematik Universtaet Essen 10, 149-159 (1983).(MR 85g,47046)

Eigenvector expansion in multiparameter eigenvalue problems,
Shiva Mathematics Series 8, 93-101 (1984).

On the differential equation y”+exp(y^m-t)=0, in Trends and Developmentsin Ordinary Differential Equations (eds. Y. Alavi and P.-H. Hsieh),379-381, World Scientific, 1994.