
RESEARCH INTERESTS
Current main interests are in the asymptotic behavior and
oscillation theory of ordinary differential and difference
equations; numerical linear algebra; Toeplitz, Hankel, and other
special functions, data smoothing.
RESEARCH PUBLICATIONS
 1.
On an explicit method for the solution of a Stefan problem, J. Soc.
Indus. Appl. Math. 7 (1959), 184204 (doctoral thesis).
 2.
On periodicities of certain sequences of residues, Amer. Math.
Monthly 67 (1960), 652656.
 3.
Stability of the snowplow differential equation representing the
expansion of a plasma bubble, Chap. 10 of Theoretical study of
hydromagnetic
stability and turbulence, Annual Report #AFSWCTDR6212 for the period
January 1December 31, 1961, Radio Corp. of America. Missile and
Surface
Radar Div., Moorestown, N.J., with Martin Kruskal.
 4.
A general class of discrete timeinvariant filters, J. Soc. Indust.
Appl. Math. 9 (1961), 405421.
 5.
On the asymptotic behavior of solutions of second order linear
differential equations, Proc. Amer. Math. Soc. 14 (1963),
1214.
 6.
An algorithm for the inversion of finite Toeplitz matrices, J. Soc.
Indust. Appl. Math. 12 (1964), 515522.
 7.
An algorithm for the inversion of finite Hankel matrices, J. Soc.
Indust. Appl. Math. 13 (1965), 11021107.
 8.
On the extrapolation of a special class of stationary time series,
Ann. Math. Stat. 36 (1965), 14261432.
 9.
On the inversion of a Hilbert type matrix, SIAM Review 8 (1966),
5761 (with P. A. Scheinok).
 10.
On the stability of midpoint smoothing with Legendre polynomials,
Proc. Amer. Math. Soc. 18 (1967), 191199.
 11.
Bounds on the generating functions of certain smoothing
operations, Proc. Amer. Math. Soc. 18 (1967), 200206.
 12.
Research in methods of generating Liapunov functions, Final report
# NASACR61437, 1967 with R. Drake and E. Norman.
 13.
A data combination method for postflight trajectory analysis, J.
Spacecraft and Rockets 41 (1967), 424427.
 14.
Weighting coefficients for the prediction of stationary time
series from the finite past, SIAM J. Appl. Math. 15 (1967),
15021510.
 15.
Stability of certain differential equations with homogeneous right
hand sides, J. Diff. Eqns. 5 (1969), 470475 (with E. Norman).
 16.
Continuous smoothing with polynomial weighting, SIAM J. Appl.
Math. 19 (1970), 382389.
 17.
Discrete minimum variance smoothing of a polynomial plus
random noise, J. Math. Anal. Appl. 35 (1971), 630645.
 18.
Stability of a class of discrete minimum variance smoothing
formulas, SIAM J. Numer. Anal. 9 (1972), 307315.
 19.
Asymptotic behavior of solutions of Lu=g(t,u,dots,u^(k1)), J.
Diff. Eqns. 11 (1972), 3848.
 20.
Asymptotic behavior of solutions of perturbed disconjugate
equations, J. Diff. Eqns. 11 (1972), 661671.
 21.
Strong discrete minimum variance estimation of a polynomial plus
random noise, J. Math. Anal. Appl. 41 (1973), 2033.
 22.
Nonnegative and alternating expansions of one set of orthogonal
polynomials in terms of another, SIAM J. Math. Anal. 4 (1973),
111115.
 23.
Canonical forms and principal systems for general disconjugate
equations, Trans. Amer. Math. Soc. 189 (1974), 319327.
 24.
Inversion of Toeplitz band matrices, Math. Comp. 28 (1974),
10891098.
 25.
A sufficient condition for eventual disconjugacy, Proc. Amer.
Math. Soc. 52 (1975), 139146.
 26.
Proof of a conjecture of Askey on orthogonal expansions with
positive coefficients, Bull. Amer. Math. Soc. 82 (1975),
954956.
 27.
Oscillation properties of perturbed disconjugate equations, Proc.
Amer. Math. Soc. 52 (1976), 147155.
 28.
Asymptotic integration of linear differential equations subject to
integral smallness conditions involving ordinary convergence, SIAM
J. Math. Anal. 7 (1976), 213221.
 29.
Orthogonal polynomial expansions with nonnegative coefficients,
SIAM J. Math. Anal. 7 (1976), 824833.
 30.
Band matrices with Toeplitz inverses, Linear Algebra Appl. 27
(1979), 199210 (with T. N. E. Greville). (Also, Transactions of
the
TwentyFourth Conference of Army Mathematicians, (1978) 365375, and
Selected
Papers of T. N. E. Greville, Charles Babbage Research Centre, Winnepeg,
Canada,
1984.)
 31.
Interpolating functions associated with second order differential
equations, Proc. Amer. Math. Soc. 78 (1980), 253258.
 32.
Limits of certain sequences associated with cylinder functions,
Houston J. Math. 7 (1981), 289294.
 33.
An oscillation condition for differential equations of arbitrary
order, Proc. Amer. Math. Soc. 82 (1981), 548552.
 34.
Asymptotic theory of perturbed general disconjugate equations,
Hiroshima Math J. 12 (1982), 4358.
 35.
Systems of differential equations subject to mild integral
smallness conditions, Proc. Amer. Math. Soc. 87 (1983),
263270.
 36.
Asymptotic integration of y^(n) +p(t)y^gamma =f(t) under mild
integral smallness conditions, Funkcial. Eckvac. 26 (1983),
197209.
 37.
Eventual disconjugacy of a linear differential equation, Proc.
Amer. Math. Soc. 89 (1983), 461466.
 38.
Asymptotic behavior of solutions of an nth order differential
equation, Rocky Mountain J. Math. 14 (1984), 441450.
 39.
Asymptotic integration of linear differential equations subject to
mild integral conditions, SIAM J. Math. Anal. 15 (1984),
932942.
 40.
Asymptotic theory of perturbed general disconjugate equations II,
Hiroshima Math. J. 14 (1984), 169187.
 41.
Asymptotics of differential systems with deviating arguments,
Proc. Amer. Math. Soc. 92 (1984), 219224.
 42.
Functional perturbations of second order differential equations,
SIAM J. Math. Anal. 16 (1985), 741756.
 43.
On the eigenvalue problem for Toeplitz band matrices, Linear
Algebra Appl. 64 (1985), 199214.
 44.
On the eigenvalue problem for Toeplitz matrices generated by
rational functions, Lin. Multilin. Algebra 19 (1985), 169185.
 45.
Explicit inversion formulas for Toeplitz band matrices, SIAM J.
Alg. Disc. Meth. 6 (1985), 546554.
 46.
Eventual disconjugacy of a linear differential equation II, Proc.
Amer. Math. Soc. 94 (1985), 629635.
 47.
Global existence theorems for solutions of nonlinear differential
equations with prescribed asymptotic behavior, J. London Math. Soc.
31 (1985), 478486 (with T. Kusano).
 48.
On the eigenvalue problem for a class of band matrices including
those with Toeplitz inverses, SIAM J. Alg. Disc. Meth. 7 (1986),
167179.
 49.
Solution of systems with Toeplitz matrices generated by rational
functions, Linear Algebra Appl. 74 (1986), 191211.
 50.
On t_\infty quasisimilarity of linear systems, Ann. di Mat.
Pura ed Appl. 142 (1985), 293302.
 51.
Existence of global solutions with prescribed asymptotic behavior
for nonlinear differential equations, Ann. di Mat. Pura ed Appl. 142
(1985), 381392 (with T. Kusano).
 52.
Extensions of a theorem of Wintner on systems with asymptotically
constant solutions, Trans. Amer. Math. Soc. 293 (1986),
477483.
 53.
Existence and nonoscillation theorems for an EmdenFowler equation
with deviating argument, Trans. Amer. Math. Soc. 294 (1986),
217232.
 54.
Linear perturbations of a nonoscillatory second order equation,
Proc. Amer. Math. Soc. 97 (1986), 423428.
 55.
Linear perturbations of general disconjugate equations,
Proceedings of Equadiff 6, The Czechoslovak Conference on Differential
Equations and Their Applications, SpringerVerlag.
 56.
Global existence of solutions of mixed sublinearsuperlinear
differential equations, Hiroshima Math. J. 16 (1986), 597606 (with
T. Kusano).
 57.
Linear perturbations of a constant coefficient differential
equation subject to mild integral smallness conditions, Czechoslovak
Math. J. 36 (1986), 623633.
 58.
A note on solving nearly triangular Toeplitz systems, Linear
Algebra Appl. 93 (1987), 5765.
 59.
First integrals for equations with nonlinearities of the
EmdenFowler type,
Int. J. Nonlinear Mech. 22 (1987), 217226 (with
L. Y. Bahar).
 60.
Global existence of nonoscillatory solutions of perturbed general
disconjugate equations, Hiroshima Math. J. 17 (1987), 415431 (with
Kusano)
 61.
Characteristic polynomials of symmetric rationally generated
Toeplitz matrices, Lin. Multilin. Alg. 21 (1987), 289296.
 62.
Toeplitz systems associated with the product of a formal Laurent
series and a Laurent polynomial, SIAM J. Matrix Th. Appl. 9 (1988),
181193.
 63.
Numerical solution of the eigenvalue problem for symmetric
rationally generated Toeplitz matrices, in Linear Algebra in
Signals,
Systems and Control rm ed. by B. N. Datta, et. al. and as an invited
paper in a special issue of SIAM J. Matrix Th. Appl. 9 (1988),
291303.
 64.
Asymptotic integration of a perturbed constant coefficient
differential equation under mild integral smallness conditions, SIAM
J. Math. Anal. 19 (1988), 444459.
 65.
Efficient application of the SchauderTychonoff theorem to
functional perturbations of x^(n) =0, Funkcial. Ekvac. 31 (1988),
161178.
 66.
Systems of functional differential equations with asymptotically
constant solutions, Proc. Amer. Math. Soc. 104 (1988), 10911097
(with T. Kusano).
 67.
Numerical solution of the eigenvalue problem for Hermitian
Toeplitz matrices, SIAM J. Matrix Anal. Appl. 10 (1989),
135156.
 68.
General functional differential systems with asymptotically
constant solutions, Differential and Integral Equations 2 (1989),
405410.
 69.
Mixed sublinear, superlinear, and singular systems of functional
differential equations, Differential Equations and Applications
(Proceedings of the International Conference on Theory and
Applications of Differential Equations, Ohio University, 1988),
448453.
 70.
A note on a Toeplitz inversion formula, Linear
Algebra Appl. 129 (1990), 5562.
 71.
Efficient application of the SchauderTychonoff theorem to systems of
functional
differential equations (free download from Elsevier), J. Math. Anal.
Appl.
150 (1990), 246263.
 72.
Spectral evolution of a oneparameter extension of a real
symmetric Toeplitz matrix, SIAM J. Matrix Anal. Appl. 11 (1990),
601611.
 73.
Explicit weighting coefficients for predicting ARMA time series
from the finite past,
J. Comp. Appl. Math. 34 (1991), 251262.
 74.
Numerical solution of the eigenvalue problem for efficiently
structured Hermitian matrices, Linear Algebra Appl. 154156
(1991), 415432.
 75.
Mild integrability conditions for global solutions of an elliptic
equation, J. Comp. Appl. Math. 39 (1992), 3948.
 76.
Asymptotic behavior of solutions of a linear second order
difference equation,
J. Comp. Appl. Math. 41 (1992), 95103.
 77.
Global solutions of nonlinear differential equations, in World
Scientific Series in Applicable Analysis, vol. 1 (1992), 543557,
Recent Trends in Differential Equations, dedicated to Professor V. I.
Lakshmikantham on his 65th birthday.
 78.
A note on computing eigenvalues of banded Hermitian Toeplitz
matrices, SIAM J. Sci. Stat. Comput. 14 (1993), 248252.
 79.
Existence of solutions of functionaldifferential systems with
prescribed asymptotic behavior, Proc. Fourth International
Conference
on Differential Equations, 148158 (Rousse, Bulgaria, 1319
August, 1989); edited by P. Popivanov and S. Tersian.
 80.
Asymptotic behavior of solutions of functionally perturbed
nonoscillatory second order differential equations, Dynamical
Systems,
Proceedings of the Special Program at Nankai Institute of Mathematics
held at Nankai University, Tianjin, People's Republic of China, 1991,
221236. Published by World Scientific, Singapore, New Jersey,
London , Hong Kong; edited by L. ShanTao, Y. YanQian, D.
TongRen.
 81.
Asymptotic behavior of solutions of Poincar'e difference
equations, Proc. Amer. Math. Soc. 119 (1993), 431438.
 82.
Asymptotic behavior of solutions of EmdenFowler difference
equations with oscillating coefficients,
J. Math. Anal. Appl. 179 (1993), 135153.
 83.
Interlacement of the even and odd spectra of real symmetric
Toeplitz matrices, Linear Algebra Appl., 195 (1993), 5968.
 84.
Some spectral properties of Hermitian Toeplitz matrices, SIAM J.
Matrix Anal. Appl. 15 (1994), 938942.
 85.
Asymptotic behavior of solutions of Poincar'e recurrence systems,
Computers Math. Applic., 28 (1994), 317324.
 86.
Invertibly convergent infinite products of matrices, with
applications to difference equations, Computers Math. Applic. 30
(1995), 3946.
 87.
Asymptotic behavior of solutions of asymptotically constant coefficient
systems
of linear differential equations (free download from Elsevier),
Computers
Math. Applic. 30 (1995), 111117.
 88.
Numerical solution of the inverse eigenvalue problem for real
symmetric Toeplitz matrices, SIAM J. Sci. Comp. 18 (1997),
17221736.
 89.
Linear asymptotic equilibrium and uniform, exponential, and strict
stability of linear difference systems,
Computers Math. Applic.
36 (1998) 261267.
 90.
Trench's canonical form for a disconjugate nthorder linear
difference equation, Pan American J. Math. 8 (1998), 5571 (with
B.Harris and R.Krueger).
 91.
Invertibly convergent infinite products of matrices (free download
from
Elsevier), J. Comp. Appl. Math. 101 (1999), 255263.
 92.
Asymptotic distribution of the spectra of a class of generalized
KacMurdockSzeg"o matrices,
Linear Algebra Appl. 294 (1999), 181192.
 93.
Conditional convergence of infinite products, American
Mathematical Monthly 106 (1999), 646651.
 94.
Asymptotic distribution of the even and odd spectra of real
symmetric Toeplitz matrices,
Linear Algebra Appl. 302303 (1999),
155162.
 95.
Linear asymptotic equilibrium for nilpotent systems of difference
equations, J. Difference Equations Appl. 5 (1999), 549556.
 96.
Systems of difference equations with asymptotically constant
solutions, Lakshmikantham's Legacy, Nonlinear Analysis, Theory,
Methods, and Applications, 40 (2000), 611615.
 97.
Linear perturbations of a nonoscillatory second order difference
equation,
J. Math. Anal. Appl. 255 (2001), 627635.
 98.
Properties of some generalizations of KacMurdockSzëgo matrices,
Structured Matrices in Mathematics, Computer Science II Control,
Signal and Image Processing (AMS Contemporary Mathematics Series), 281
(2001), 233245.
 99.
Spectral distribution of generalized KacMurdockSzëgo matrices,
Linear Algebra Appl. 347 (2002), 251273.
 100.
Asymptotically constant solutions of functional difference
systems, J. Difference Eq. Appl., 8 (2002), 811821.
 101.
Linear perturbations of a nonoscillatory second order difference
equation II, J. Math. Anal. Appl., 273 (2002), 548557.
 102.
Linear perturbations of a nonoscillatory second order
differential equation II, Proc. Amer. Math. Soc., 131 (2003),
14151422.
 103.
Absolute equal distribution of the spectra of Hermitian matrices,
Linear Algebra Appl., 366 (2003), 417431.
 104.
Absolute equal distribution of families of finite sets (free download
from
Elsevier), Linear Algebra Appl. 367 (2003), 131146.
 105.
Spectral distribution of Hermitian Toeplitz matrices formally
generated by rational functions, Fast Algorithms for Structured
Matrices: Theory and Applications, (Ed. Vadim Olshevsky), Contemporary
Mathematics, Vol. 323, American Mathematical Society, 2003,
323327.
 106.
A note on asymptotic zero distribution of orthogonal polynomials,
Linear Algebra Appl. 375 (2003) 275281.
 107.
Characterization and properties of matrices with generalized
symmetry or skew symmetry, Linear Algebra Appl. 377 (2004)
207218.
 108.
Inverse eigenproblems and associated approximation problems for
matrices with generalized symmetry or skew symmetry (free download
from
Elsevier), Linear Algebra Appl. 380 (2004), 199211.
 109.
An elementary note on asymptotic properties of Toeplitz and
multilevel Toeplitz matrices, Linear Algebra Appl. 382 (2004)
231235.
 110.
Hermitian, Hermitian Rsymmetric, and Hermitian Rskew symmetric
Procrustes problems, Linear Algebra Appl. 387 (2004) 8398.
 111.
Minimization problems for (R,S)symmetric and (R,S)skew
symmetric matrices, Linear Algebra Appl. 389 (2004) 2331.
 112.
Simplification and strengthening of Weyl's definition of
asymptotic equal distribution of two families of finite sets, Cubo A
Mathematical Journal Vol. 06 N 3 (2004), 4754.
 113.
Asymptotic relationships between singular values of structured
matrices similarly generated by different formal expansions of a
rational function, Numer. Linear Algebra Appl. 12 (2005),
111116.
 114.
Characterization and properties of (R,S)symmetric, (R,S)skew
symmetric, and (R,S)conjugate matrices,
SIAM J. Matrix Anal Appl. 26 (2005) 748757.
 115.
Multilevel matrices with involutory symmetries and skew
symmetries, Linear Algebra Appl. 403 (2005) 5374.
 116.
Functional perturbations of nonoscillatory second order
difference equations, Dynamic Systems and Applications 15 (2006)
155171.
 117.
Absolute equal distribution of the eigenvalues of discrete
SturmLiouville problems,
J. Math. Anal. Appl. 321 (1) (2006) 299307.
 118.
Asymptotic spectral properties of totally symmetric multilevel
Toeplitz matrices,
Linear Algebra Appl. 416 696709 (2006).
 119.
Characterization and properties of matrices with kinvolutory
symmetries, Linear Algebra Appl. 429, Issues 89 (2008)
22782290.
 120.
Properties of unilevel block circulants, Linear Algebra Appl. 430
(2009)
20122025.
 121.
Properties of multilevel block circulants, Linear Algebra Appl.
431 (2009) 18331847.
 122.
On nonautonomous linear systems of differential
and difference equations with
Rsymmetric coefficient matrices, Linear Algebra Appl.
431 (2009) 21092117.
 123.
Characterization and properties of matrices with kinvolutory
symmetries II, Linear Algebra Appl. 432 (2010), 27822797.
 124.
Asymptotic preconditioning of linear homogeneous
systems of differential equations,
Linear Algebra Appl. 434 (2011), 16311637.
 125.
Inverse problems for unilevel block alphacirculants,
Numerical Linear Algebra Appl., DOI: 10.1002/nla.832, Online December 2011.
 126.
Characterization and properties of (R,S_\sigma)commutative matrices,
Linear Algebra Appl.,
Linear Algebra Appl. 436 (2012), no. 11, 42614278.
 127.
An elementary view of Weyl's theory of equal distribution,
American Mathematical Monthly, 119 (2012), 852861.
UNPUBLISHED, BUT PERHAPS USEFUL
 1.
The relationship between Trench's Toeplitz inversion
algorithm and the GohbergSemencul formula
.
 2.
A special case of the method of Frobenius
.
 3.
Notes on the real symmetric Toeplitz eigenvalue problem.
 4.
Numerical solution of the eigenvalue problem for Hermitian
Toeplitzlike matrices
 5.
A Matlab package for the real symmetric Toeplitz inverse eigenvalue
problem.
 6.
Inverses of lower triangular Toeplitz matrices.
 7.
Spectral decomposition of KacMurdockSzego matrices.
 8.
A Matlab procedure
for spectral decomposition of real symmetric Toeplitz matrices.
 9.
A Riemann integral proof of a generalized Riemann lemma.
 10.
Efficient application of the SchauderTychonoff theorem to functional
differential systems.
 11.
On matrices with rotative symmetries.
 12.
Banded symmetric Toeplitz
matrices: where
linear algebra borrows from difference equations.
 13.
Linear differential
systems
with coefficient matrices that commute
with a spectrally separated matrix function.
