## Hinton, Don Barker

Compute Distance To:
 Author ID: hinton.don-barker Published as: Hinton, D. B.; Hinton, Don; Hinton, Don B.; Hinton, Don Barker; Hinton, D. more...less
 Documents Indexed: 135 Publications since 1966 1 Contribution as Editor Co-Authors: 40 Co-Authors with 107 Joint Publications 736 Co-Co-Authors
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### Co-Authors

 29 single-authored 30 Shaw, J. K. 27 Brown, Richard Clark 12 Behncke, Horst 11 Lewis, Roger T. 10 Klaus, Martin 7 Ahlbrandt, Calvin D. 5 Clark, Steve 4 Clark, Stephen L. 4 Everitt, William Norrie 3 Schneider, Albert 3 Shaw, Ken 2 Anderson, Terry G. 2 Belinsky, Boris P. 2 Kauffman, Robert M. 2 Krall, Allan M. 2 McCarthy, Maeve Lewis 1 Ashbaugh, Mark S. 1 Bailey, Paul B. 1 Bradley, John S. 1 Burenkov, Viktor Ivanovich 1 Collier Melescue, Suzanne 1 Das, Jyoti 1 Edmunds, David Eric 1 Fink, Arlington Michael 1 Heidel, J. W. 1 Khan, Mohammad M. S. 1 Kufner, Alois 1 Kwong, Man Kam 1 Littlejohn, Lance L. 1 Markett, Clemens 1 Nichols, Roger 1 Rákosník, Jiří 1 Read, Thomas T. 1 Remling, Christian 1 Schaefer, Philip W. 1 Schwabik, Štefan 1 Shaw, Ming-Fu 1 Weerasena, Lakmali 1 Wong, James S. W. 1 Zettl, Anton
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### Serials

 8 Journal of Differential Equations 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 Journal of Mathematical Analysis and Applications 6 Canadian Journal of Mathematics 6 Proceedings of the London Mathematical Society. Third Series 5 Mathematische Nachrichten 5 Proceedings of the American Mathematical Society 5 The Quarterly Journal of Mathematics. Oxford Second Series 5 Differential and Integral Equations 5 SIAM Journal on Mathematical Analysis 3 Applicable Analysis 3 Rocky Mountain Journal of Mathematics 3 Quaestiones Mathematicae 2 Canadian Mathematical Bulletin 2 Journal of Computational and Applied Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Dynamic Systems and Applications 2 Journal of Inequalities and Applications 2 Mathematical Inequalities & Applications 2 Journal of Spectral Theory 1 Computers & Mathematics with Applications 1 Inverse Problems 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Časopis Pro Pěstování Matematiky 1 Duke Mathematical Journal 1 Funkcialaj Ekvacioj. Serio Internacia 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Real Analysis Exchange 1 Studies in Applied Mathematics 1 Transactions of the American Mathematical Society 1 Mathematica Bohemica 1 Journal of the Australian Mathematical Society. Series A 1 Advances in Differential Equations 1 Electronic Journal of Qualitative Theory of Differential Equations 1 Lecture Notes in Pure and Applied Mathematics 1 Operators and Matrices
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### Fields

 111 Ordinary differential equations (34-XX) 47 Operator theory (47-XX) 23 Real functions (26-XX) 10 Mechanics of particles and systems (70-XX) 5 Difference and functional equations (39-XX) 3 Partial differential equations (35-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Quantum theory (81-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 General topology (54-XX)

### Citations contained in zbMATH Open

109 Publications have been cited 1,156 times in 714 Documents Cited by Year
On Titchmarsh-Weyl $$M(\lambda)$$-functions for linear Hamiltonian system. Zbl 0472.34014
Hinton, D. B.; Shaw, J. K.
1981
Spectral analysis of second order difference equations. Zbl 0392.39001
Hinton, Don B.; Lewis, Roger T.
1978
An expansion theorem for an eigenvalue problem with eigenvalue parameter in the boundary condition. Zbl 0427.34023
Hinton, Don B.
1979
Opial’s inequality and oscillation of second order equations. Zbl 0866.34026
Brown, R. C.; Hinton, D. B.
1997
On the Titchmarsh-Weyl coefficients for singular $$S$$-Hermitian systems. I. Zbl 0806.34023
Hinton, D. B.; Schneider, A.
1993
On the spectrum of a singular Hamiltonian system. Zbl 0509.34018
Hinton, D. B.; Shaw, J. K.
1982
Hamiltonian systems of limit point or limit circle type with both endpoints singular. Zbl 0476.34027
Hinton, D. B.; Shaw, J. K.
1983
Oscillation theory for generalized second-order differential equations. Zbl 0485.34021
Hinton, Don B.; Lewis, Roger T.
1980
On boundary value problems for Hamiltonian systems with two singular points. Zbl 0539.34016
Hinton, D. B.; Shaw, J. K.
1984
Lyapunov inequalities and their applications. Zbl 1034.34002
Brown, Richard C.; Hinton, Don B.
2000
The effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theory. Zbl 0459.34018
Ahlbrandt, Calvin D.; Hinton, Don B.
1981
Discrete spectra criteria for singular differential operators with middle terms. Zbl 0298.34018
Hinton, Don B.; Lewis, Roger T.
1975
Asymptotic behavior of solutions of $$(ry^{(m)})^{(k)} \pm qy = 0$$. Zbl 0175.38101
Hinton, D. B.
1968
Parameterization of the $$M(\lambda)$$ function for a Hamiltonian system of limit circle type. Zbl 0532.34011
Hinton, D. B.; Shaw, J. K.
1983
Singular differential operators with spectra discrete and bounded below. Zbl 0418.47021
Hinton, Don B.; Lewis, Roger T.
1979
The spectrum of differential operators of order $$2n$$ with almost constant coefficients. Zbl 0990.34070
Behncke, Horst; Hinton, Don; Remling, Christian
2001
Disconjugate properties of a system of differential equations. Zbl 0161.27904
Hinton, D. B.
1966
On the strong limit-n classification of linear ordinary differential expressions of order 2n. Zbl 0305.34040
Everitt, W. N.; Hinton, D. B.; Wong, J. S. W.
1974
Eigenfunctions, deficiency indices and spectra of odd-order differential operators. Zbl 1158.34050
Behncke, Horst; Hinton, D. B.
2008
Necessary and sufficient conditions for the discreteness of the spectrum of certain singular differential operators. Zbl 0462.47030
Ahlbrandt, Calvin D.; Hinton, Don B.; Lewis, Roger T.
1981
A Liapunov inequality for linear Hamiltonian systems. Zbl 0909.34033
Clark, Steve; Hinton, Don
1998
On the spectrum of a singular Hamilton system. II. Zbl 0615.34016
Hinton, D. B.; Shaw, J. K.
1986
Absolutely continuous spectra of Dirac systems with long range, short range and oscillating potentials. Zbl 0571.34017
Hinton, D. B.; Shaw, J. K.
1985
On the Titchmarsh-Weyl coefficients for singular S-Hermitian systems. II. Zbl 0869.34019
Hinton, D. B.; Schneider, A.
1997
Limit point criteria for differential equations. Zbl 0229.34024
Hinton, Don
1972
Absolutely continuous spectra of second order differential operators with short and long range potentials. Zbl 0583.34017
Hinton, D. B.; Shaw, J. K.
1986
Sturm’s 1836 oscillation results evolution of the theory. Zbl 1120.34020
Hinton, Don
2005
Deficiency indices of odd-order differential operators. Zbl 0417.47018
Hinton, Don B.
1978
Discrete Lyapunov inequalities. Zbl 0940.39013
Clark, Steve; Hinton, Don
1999
A Stieltjes-Volterra integral equation theory. Zbl 0142.09401
Hinton, D. B.
1966
Spectral theory of Hamiltonian systems with almost constant coefficients. Zbl 1237.34141
Behncke, Horst; Hinton, Don
2011
The asymptotic form of the Titchmarsh-Weyl coefficient for Dirac systems. Zbl 0489.34010
Everitt, W. N.; Hinton, D. B.; Shaw, J. K.
1983
Embedded halfbound states for potentials of Wigner-von Neumann type. Zbl 0689.34018
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1991
On the eigenfunction expansions of singular ordinary differential equations. Zbl 0405.34025
Hinton, Don B.
1977
Applications of a one-dimensional Sobolev inequality to eigenvalue problems. Zbl 0842.34083
Brown, R. C.; Hinton, D. B.; Schwabik, Š.
1996
Sufficient conditions for weighted inequalities of sum form. Zbl 0587.26011
Brown, R. C.; Hinton, D. B.
1985
Series representation and asymptotics for Titchmarsh-Weyl m-functions. Zbl 0715.34044
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1989
Eigenfunction expansions for a singular eigenvalue problem with eigenparameter in the boundary condition. Zbl 0458.34014
Hinton, Don
1981
Weighted interpolation inequalities of sum and product form in $${\mathbb{R}}^ n$$. Zbl 0648.26008
Brown, R. C.; Hinton, D. B.
1988
The existence of oscillatory solutions for a nonlinear differential equation. Zbl 0243.34062
Heidel, J. W.; Hinton, Don B.
1972
Limit point criteria for differential equations. II. Zbl 0249.34010
Hinton, Don
1974
Limit point-limit circle criteria for $$(py')'+qy=\lambda ky$$. Zbl 0337.34019
Hinton, Don
1974
A criterion for n-n oscillation in differential equations of order 2n. Zbl 0157.15001
Hinton, D. B.
1968
Some disconjugacy criteria for differential equations with oscillatory coefficients. Zbl 1101.34018
Clark, Stephen; Hinton, Don
2005
On the number of eigenvalues in the spectral gap of a Dirac system. Zbl 0618.34024
Hinton, D. B.; Mingarelli, A. B.; Read, T. T.; Shaw, J. K.
1986
Levinson’s theorem and Titchmarsh-Weyl m($$\lambda$$ ) theory for Dirac systems. Zbl 0652.34030
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1988
Eigenfunction expansions and spectral matrices of singular differential operators. Zbl 0389.34021
Hinton, Don B.
1978
The fourth-order Bessel-type differential equation. Zbl 1053.34013
Das, Jyoti; Everitt, W. N.; Hinton, D. B.; Littlejohn, L. L.; Markett, C.
2004
Half-bound states and Levinson’s theorem for discrete systems. Zbl 0822.47032
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1991
Differential operators with spectral parameter incompletely in the boundary conditions. Zbl 0715.34133
Hinton, D. B.; Shaw, J. K.
1990
Weighted interpolation inequalities and embeddings in $$R^ n$$. Zbl 0726.26012
Brown, R. C.; Hinton, D. B.
1990
Two singular point linear Hamiltonian systems with an interface condition. Zbl 1198.34011
Behncke, Horst; Hinton, Don
2010
Dirac systems with discrete spectra. Zbl 0607.34020
Hinton, D. B.; Shaw, J. K.
1987
Principal solutions of positive linear Hamiltonian systems. Zbl 0347.34008
Hinton, Don
1976
High-energy asymptotics for the scattering matrix on the line. Zbl 0733.34083
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1989
On the minimization of singular quadratic functionals. Zbl 0456.49019
Bradley, John S.; Hinton, Don B.; Kauffman, Robert M.
1981
On the absolutely continuous spectrum of the perturbed Hill’s equation. Zbl 0528.34027
Hinton, D. B.; Shaw, J. K.
1985
Boundary conditions for differential operators with intermediate deficiency index. Zbl 0627.34023
Hinton, Don; Krall, Allan M.; Shaw, Ken
1987
A weighted Hardy’s inequality and nonoscillatory differential equations. Zbl 0766.26013
Brown, R. C.; Hinton, D. B.
1992
Strong limit-point and Dirichlet criteria for ordinary differential expressions of order 2n. Zbl 0348.34014
Hinton, Don
1977
Two separation criteria for second order ordinary or partial differential operators. Zbl 0937.34068
Brown, R. C.; Hinton, D. B.
1999
Weighted interpolation and Hardy inequalities with some spectral theoretic applications. Zbl 0858.26010
Brown, R. C.; Hinton, D. B.
1994
Some separation criteria and inequalities associated with linear second order differential operators. Zbl 0982.34032
Brown, R. C.; Hinton, D. B.; Shaw, M. F.
2000
Asymptotic phase, asymptotic modulus, and Titchmarsh-Weyl coefficient for a Dirac system. Zbl 0738.34044
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1989
On the spectral representation for singular selfadjoint boundary eigenvalue problems. Zbl 0911.34018
Hinton, Don; Schneider, Albert
1998
Relative boundedness and compactness theory for second-order differential operators. Zbl 0891.34062
Anderson, Terry G.; Hinton, Don B.
1997
Molchanov’s discrete spectra criterion for a weighted operator. Zbl 0446.47034
Hinton, Don B.
1979
Solutions of $$(ry^{(n)})^{(n)}+qy=0$$ of class $${\mathcal L}_p[0,\infty)$$. Zbl 0241.34018
Hinton, Don
1972
Some Opial, Lyapunov, and de la Valée Poussin inequalities with nonhomogeneous boundary conditions. Zbl 0955.26009
Brown, Richard C.; Fink, A. M.; Hinton, Don B.
2000
Spectral theory and computational methods of Sturm-Liouville problems. Proceedings of the 1996 conference, Knoxville, TN, USA, in conjunction with the 26th Barrett memorial lecture series. Zbl 0866.00046
1997
Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein. Zbl 1006.34078
Clark, Steve; Hinton, Don
2002
Clamped end boundary conditions for fourth-order selfadjoint differential equations. Zbl 0148.06402
Hinton, D. B.
1967
Some stability conditions for $$y''+qy = 0$$. Zbl 0155.12701
Hinton, D. B.
1968
A class of differential operators with complex coefficients and compact resolvent. Zbl 1424.34298
Behncke, Horst; Hinton, Don
2018
Titchmarsh’s lambda-dependent boundary conditions for Hamiltonian systems. Zbl 0509.34019
Hinton, Don; Shaw, Ken
1982
Absolutely continuous spectra of perturbed periodic Hamiltonian systems. Zbl 0634.34010
Hinton, D. B.; Shaw, J. K.
1987
An oscillation criterion for solutions of $$(ry')' + gy^\gamma = 0$$. Zbl 0188.15401
Hinton, Don
1969
Oscillation theory at a finite singularity. Zbl 0362.34025
Hinton, Don B.; Lewis, Roger T.
1978
Relative boundedness-compactness inequalities for a second order differential operator. Zbl 1072.34093
Hinton, Don B.; Melescue, Suzanne Collier
2001
Relative form boundedness and compactness for a second-order differential operator. Zbl 1057.34104
Brown, Richard C.; Hinton, Don B.
2004
Spectral theory of higher order differential operators by examples. Zbl 1285.34074
Behncke, Horst; Hinton, Don B.
2013
Transformation theory of symmetric differential expressions. Zbl 1160.34076
Behnke, Horst; Hinton, Don
2006
Bounds and optimization of the minimum eigenvalue for a vibrating system. Zbl 1340.34334
Hinton, Don; McCarthy, Maeve
2013
Strong nonsubordinacy and absolutely continuous spectra for Sturm- Liouville equations. Zbl 0776.34019
Clark, Steve; Hinton, Don
1993
Interpolation inequalities with power weights for functions of one variable. Zbl 0779.26012
Brown, Richard; Hinton, Don
1993
Continuous spectra of second-order differential operators. Zbl 0201.12302
Hinton, Don Barker
1970
Continuous spectra of an even order differential operator. Zbl 0285.34016
Hinton, Don
1974
Some function space inequalities and their application to oscillation and stability problems in differential equations. Zbl 1043.26007
Brown, Richard; Clark, Stephen; Hinton, Don
2002
Deficiency indices and spectral theory of third order differential operators on the half line. Zbl 1093.34047
Behncke, Horst; Hinton, Don
2005
$$\mathcal C$$-symmetric Hamiltonian systems with almost constant coefficients. Zbl 1444.34104
Behncke, Horst; Hinton, Don B.
2019
Necessary and sufficient conditions for the discreteness of the spectrum of certain singular differential operators. Zbl 0456.47036
Ahlbrandt, Calvin D.; Hinton, Don B.; Lewis, Roger T.
1980
Titchmarsh-Weyl theory for Hamiltonian systems. Zbl 0489.34020
Hinton, Don; Shaw, Ken
1981
Discreteness of some continuous spectrum eigenfunction expansions. Zbl 0799.47028
Hinton, Don B.; Kauffman, Robert M.
1993
Necessary and sufficient conditions for one variable weighted interpolation inequalities. Zbl 0627.26009
Brown, R. C.; Hinton, D. B.
1987
Asymptotics of solutions and spectra of perturbed periodic Hamiltonian systems. Zbl 0662.34054
Hinton, D. B.; Shaw, J. K.
1987
Some stability conditions for a nonlinear differential equation. Zbl 0182.11902
Hinton, D.
1969
Asymptotic formulae for linear equations. Zbl 0244.34045
Hinton, Don B.
1972
Boundary conditions for differential systems in intermediate limit situations. Zbl 0558.34017
Krall, Allan M.; Shaw, J. K.; Hinton, D. B.
1984
On the Titchmarsh-Weyl function for the half-line perturbed periodic Hill’s equation. Zbl 0706.34023
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1990
Spectrum of a Hamiltonian system with a spectral parameter in a boundary condition. Zbl 0712.70037
Hinton, D. B.; Shaw, J. K.
1987
Singular Sturm-Liouville operators with extreme properties that generate black holes. Zbl 1487.34083
Belinskiy, Boris P.; Hinton, Don B.; Nichols, Roger
2021
$$\mathcal{C}$$-symmetric second order differential operators. Zbl 1486.34165
Behncke, Horst; Hinton, Don
2020
$$\mathcal C$$-symmetric Hamiltonian systems with almost constant coefficients. Zbl 1444.34104
Behncke, Horst; Hinton, Don B.
2019
A class of differential operators with complex coefficients and compact resolvent. Zbl 1424.34298
Behncke, Horst; Hinton, Don
2018
Spectral theory of higher order differential operators by examples. Zbl 1285.34074
Behncke, Horst; Hinton, Don B.
2013
Bounds and optimization of the minimum eigenvalue for a vibrating system. Zbl 1340.34334
Hinton, Don; McCarthy, Maeve
2013
Spectral theory of Hamiltonian systems with almost constant coefficients. Zbl 1237.34141
Behncke, Horst; Hinton, Don
2011
Two singular point linear Hamiltonian systems with an interface condition. Zbl 1198.34011
Behncke, Horst; Hinton, Don
2010
Some one variable weighted norm inequalities and their applications to Sturm-Liouville and other differential operators. Zbl 1266.34038
Brown, Richard C.; Hinton, Don B.
2009
Eigenfunctions, deficiency indices and spectra of odd-order differential operators. Zbl 1158.34050
Behncke, Horst; Hinton, D. B.
2008
Transformation theory of symmetric differential expressions. Zbl 1160.34076
Behnke, Horst; Hinton, Don
2006
Sturm’s 1836 oscillation results evolution of the theory. Zbl 1120.34020
Hinton, Don
2005
Some disconjugacy criteria for differential equations with oscillatory coefficients. Zbl 1101.34018
Clark, Stephen; Hinton, Don
2005
Deficiency indices and spectral theory of third order differential operators on the half line. Zbl 1093.34047
Behncke, Horst; Hinton, Don
2005
The fourth-order Bessel-type differential equation. Zbl 1053.34013
Das, Jyoti; Everitt, W. N.; Hinton, D. B.; Littlejohn, L. L.; Markett, C.
2004
Relative form boundedness and compactness for a second-order differential operator. Zbl 1057.34104
Brown, Richard C.; Hinton, Don B.
2004
Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein. Zbl 1006.34078
Clark, Steve; Hinton, Don
2002
Some function space inequalities and their application to oscillation and stability problems in differential equations. Zbl 1043.26007
Brown, Richard; Clark, Stephen; Hinton, Don
2002
On the location of the least point of the essential spectrum. Zbl 1019.34080
Hinton, Don
2002
The spectrum of differential operators of order $$2n$$ with almost constant coefficients. Zbl 0990.34070
Behncke, Horst; Hinton, Don; Remling, Christian
2001
Relative boundedness-compactness inequalities for a second order differential operator. Zbl 1072.34093
Hinton, Don B.; Melescue, Suzanne Collier
2001
Lyapunov inequalities and their applications. Zbl 1034.34002
Brown, Richard C.; Hinton, Don B.
2000
Some separation criteria and inequalities associated with linear second order differential operators. Zbl 0982.34032
Brown, R. C.; Hinton, D. B.; Shaw, M. F.
2000
Some Opial, Lyapunov, and de la Valée Poussin inequalities with nonhomogeneous boundary conditions. Zbl 0955.26009
Brown, Richard C.; Fink, A. M.; Hinton, Don B.
2000
Discrete Lyapunov inequalities. Zbl 0940.39013
Clark, Steve; Hinton, Don
1999
Two separation criteria for second order ordinary or partial differential operators. Zbl 0937.34068
Brown, R. C.; Hinton, D. B.
1999
Second order Opial inequalities in $${\mathcal L}^p$$ spaces and applications. Zbl 0981.26018
Brown, Richard; Burenkov, Victor; Clark, Steve; Hinton, Don
1999
A Liapunov inequality for linear Hamiltonian systems. Zbl 0909.34033
Clark, Steve; Hinton, Don
1998
On the spectral representation for singular selfadjoint boundary eigenvalue problems. Zbl 0911.34018
Hinton, Don; Schneider, Albert
1998
Opial’s inequality and oscillation of second order equations. Zbl 0866.34026
Brown, R. C.; Hinton, D. B.
1997
On the Titchmarsh-Weyl coefficients for singular S-Hermitian systems. II. Zbl 0869.34019
Hinton, D. B.; Schneider, A.
1997
Relative boundedness and compactness theory for second-order differential operators. Zbl 0891.34062
Anderson, Terry G.; Hinton, Don B.
1997
Spectral theory and computational methods of Sturm-Liouville problems. Proceedings of the 1996 conference, Knoxville, TN, USA, in conjunction with the 26th Barrett memorial lecture series. Zbl 0866.00046
1997
Perturbation theory for a one-term weighted differential operator. Zbl 0880.34057
Anderson, T. G.; Brown, R. C.; Hinton, D. B.
1997
Sufficient conditions for three weight sum inequalities in Lebesgue spaces. Zbl 0879.26053
Brown, R. C.; Hinton, D. B.; Kufner, A.
1997
Applications of a one-dimensional Sobolev inequality to eigenvalue problems. Zbl 0842.34083
Brown, R. C.; Hinton, D. B.; Schwabik, Š.
1996
Weighted interpolation and Hardy inequalities with some spectral theoretic applications. Zbl 0858.26010
Brown, R. C.; Hinton, D. B.
1994
An interpolation inequality and applications. Zbl 0882.26008
Brown, R. C.; Hinton, D. B.
1994
On the Titchmarsh-Weyl coefficients for singular $$S$$-Hermitian systems. I. Zbl 0806.34023
Hinton, D. B.; Schneider, A.
1993
Strong nonsubordinacy and absolutely continuous spectra for Sturm- Liouville equations. Zbl 0776.34019
Clark, Steve; Hinton, Don
1993
Interpolation inequalities with power weights for functions of one variable. Zbl 0779.26012
Brown, Richard; Hinton, Don
1993
Discreteness of some continuous spectrum eigenfunction expansions. Zbl 0799.47028
Hinton, Don B.; Kauffman, Robert M.
1993
A weighted Hardy’s inequality and nonoscillatory differential equations. Zbl 0766.26013
Brown, R. C.; Hinton, D. B.
1992
Embedded halfbound states for potentials of Wigner-von Neumann type. Zbl 0689.34018
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1991
Half-bound states and Levinson’s theorem for discrete systems. Zbl 0822.47032
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1991
Differential operators with spectral parameter incompletely in the boundary conditions. Zbl 0715.34133
Hinton, D. B.; Shaw, J. K.
1990
Weighted interpolation inequalities and embeddings in $$R^ n$$. Zbl 0726.26012
Brown, R. C.; Hinton, D. B.
1990
On the Titchmarsh-Weyl function for the half-line perturbed periodic Hill’s equation. Zbl 0706.34023
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1990
Series representation and asymptotics for Titchmarsh-Weyl m-functions. Zbl 0715.34044
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1989
High-energy asymptotics for the scattering matrix on the line. Zbl 0733.34083
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1989
Asymptotic phase, asymptotic modulus, and Titchmarsh-Weyl coefficient for a Dirac system. Zbl 0738.34044
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1989
Weighted interpolation inequalities of sum and product form in $${\mathbb{R}}^ n$$. Zbl 0648.26008
Brown, R. C.; Hinton, D. B.
1988
Levinson’s theorem and Titchmarsh-Weyl m($$\lambda$$ ) theory for Dirac systems. Zbl 0652.34030
Hinton, D. B.; Klaus, M.; Shaw, J. K.
1988
Dirac systems with discrete spectra. Zbl 0607.34020
Hinton, D. B.; Shaw, J. K.
1987
Boundary conditions for differential operators with intermediate deficiency index. Zbl 0627.34023
Hinton, Don; Krall, Allan M.; Shaw, Ken
1987
Absolutely continuous spectra of perturbed periodic Hamiltonian systems. Zbl 0634.34010
Hinton, D. B.; Shaw, J. K.
1987
Necessary and sufficient conditions for one variable weighted interpolation inequalities. Zbl 0627.26009
Brown, R. C.; Hinton, D. B.
1987
Asymptotics of solutions and spectra of perturbed periodic Hamiltonian systems. Zbl 0662.34054
Hinton, D. B.; Shaw, J. K.
1987
Spectrum of a Hamiltonian system with a spectral parameter in a boundary condition. Zbl 0712.70037
Hinton, D. B.; Shaw, J. K.
1987
On the spectrum of a singular Hamilton system. II. Zbl 0615.34016
Hinton, D. B.; Shaw, J. K.
1986
Absolutely continuous spectra of second order differential operators with short and long range potentials. Zbl 0583.34017
Hinton, D. B.; Shaw, J. K.
1986
On the number of eigenvalues in the spectral gap of a Dirac system. Zbl 0618.34024
Hinton, D. B.; Mingarelli, A. B.; Read, T. T.; Shaw, J. K.
1986
Absolutely continuous spectra of Dirac systems with long range, short range and oscillating potentials. Zbl 0571.34017
Hinton, D. B.; Shaw, J. K.
1985
Sufficient conditions for weighted inequalities of sum form. Zbl 0587.26011
Brown, R. C.; Hinton, D. B.
1985
On the absolutely continuous spectrum of the perturbed Hill’s equation. Zbl 0528.34027
Hinton, D. B.; Shaw, J. K.
1985
On boundary value problems for Hamiltonian systems with two singular points. Zbl 0539.34016
Hinton, D. B.; Shaw, J. K.
1984
Boundary conditions for differential systems in intermediate limit situations. Zbl 0558.34017
Krall, Allan M.; Shaw, J. K.; Hinton, D. B.
1984
Hamiltonian systems of limit point or limit circle type with both endpoints singular. Zbl 0476.34027
Hinton, D. B.; Shaw, J. K.
1983
Parameterization of the $$M(\lambda)$$ function for a Hamiltonian system of limit circle type. Zbl 0532.34011
Hinton, D. B.; Shaw, J. K.
1983
The asymptotic form of the Titchmarsh-Weyl coefficient for Dirac systems. Zbl 0489.34010
Everitt, W. N.; Hinton, D. B.; Shaw, J. K.
1983
On the spectrum of a singular Hamiltonian system. Zbl 0509.34018
Hinton, D. B.; Shaw, J. K.
1982
Titchmarsh’s lambda-dependent boundary conditions for Hamiltonian systems. Zbl 0509.34019
Hinton, Don; Shaw, Ken
1982
On Titchmarsh-Weyl $$M(\lambda)$$-functions for linear Hamiltonian system. Zbl 0472.34014
Hinton, D. B.; Shaw, J. K.
1981
The effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theory. Zbl 0459.34018
Ahlbrandt, Calvin D.; Hinton, Don B.
1981
Necessary and sufficient conditions for the discreteness of the spectrum of certain singular differential operators. Zbl 0462.47030
Ahlbrandt, Calvin D.; Hinton, Don B.; Lewis, Roger T.
1981
Eigenfunction expansions for a singular eigenvalue problem with eigenparameter in the boundary condition. Zbl 0458.34014
Hinton, Don
1981
On the minimization of singular quadratic functionals. Zbl 0456.49019
Bradley, John S.; Hinton, Don B.; Kauffman, Robert M.
1981
Titchmarsh-Weyl theory for Hamiltonian systems. Zbl 0489.34020
Hinton, Don; Shaw, Ken
1981
Oscillation theory for generalized second-order differential equations. Zbl 0485.34021
Hinton, Don B.; Lewis, Roger T.
1980
Necessary and sufficient conditions for the discreteness of the spectrum of certain singular differential operators. Zbl 0456.47036
Ahlbrandt, Calvin D.; Hinton, Don B.; Lewis, Roger T.
1980
An expansion theorem for an eigenvalue problem with eigenvalue parameter in the boundary condition. Zbl 0427.34023
Hinton, Don B.
1979
Singular differential operators with spectra discrete and bounded below. Zbl 0418.47021
Hinton, Don B.; Lewis, Roger T.
1979
Molchanov’s discrete spectra criterion for a weighted operator. Zbl 0446.47034
Hinton, Don B.
1979
Spectral analysis of second order difference equations. Zbl 0392.39001
Hinton, Don B.; Lewis, Roger T.
1978
Deficiency indices of odd-order differential operators. Zbl 0417.47018
Hinton, Don B.
1978
Eigenfunction expansions and spectral matrices of singular differential operators. Zbl 0389.34021
Hinton, Don B.
1978
Oscillation theory at a finite singularity. Zbl 0362.34025
Hinton, Don B.; Lewis, Roger T.
1978
On the eigenfunction expansions of singular ordinary differential equations. Zbl 0405.34025
Hinton, Don B.
1977
Strong limit-point and Dirichlet criteria for ordinary differential expressions of order 2n. Zbl 0348.34014
Hinton, Don
1977
Principal solutions of positive linear Hamiltonian systems. Zbl 0347.34008
Hinton, Don
1976
Discrete spectra criteria for singular differential operators with middle terms. Zbl 0298.34018
Hinton, Don B.; Lewis, Roger T.
1975
On the strong limit-n classification of linear ordinary differential expressions of order 2n. Zbl 0305.34040
Everitt, W. N.; Hinton, D. B.; Wong, J. S. W.
1974
Limit point criteria for differential equations. II. Zbl 0249.34010
Hinton, Don
1974
Limit point-limit circle criteria for $$(py')'+qy=\lambda ky$$. Zbl 0337.34019
Hinton, Don
1974
Continuous spectra of an even order differential operator. Zbl 0285.34016
Hinton, Don
1974
Limit-point criteria for positive definite fourth-order differential operators. Zbl 0269.34015
Hinton, Don B.
1973
Limit point criteria for differential equations. Zbl 0229.34024
Hinton, Don
1972
The existence of oscillatory solutions for a nonlinear differential equation. Zbl 0243.34062
Heidel, J. W.; Hinton, Don B.
1972
Solutions of $$(ry^{(n)})^{(n)}+qy=0$$ of class $${\mathcal L}_p[0,\infty)$$. Zbl 0241.34018
Hinton, Don
1972
Asymptotic formulae for linear equations. Zbl 0244.34045
Hinton, Don B.
1972
...and 9 more Documents
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### Cited by 595 Authors

 37 Hinton, Don Barker 24 Shi, Yuming 19 Behncke, Horst 17 Sun, Huaqing 17 Ugurlu, Ekin 16 Qi, Jiangang 16 Šimon Hilscher, Roman 14 Došlý, Ondřej 13 Gesztesy, Fritz 13 Meng, Fanwei 12 Agarwal, Ravi P. 10 Allahverdiev, Bilender Paşaoğlu 10 Chen, Shaozhu 10 Samet, Bessem 10 Zemánek, Petr 9 Evans, William Desmond 9 Everitt, William Norrie 9 Shaw, J. K. 9 Sun, Jiong 9 Zettl, Anton 8 Clark, Stephen L. 8 Kwong, Man Kam 8 Nyamwala, Fredrick Oluoch 8 Özbekler, Abdullah 7 Ahlbrandt, Calvin D. 7 Jleli, Mohamed Boussairi 7 Lewis, Roger T. 7 Markett, Clemens 7 Mogilevskii, Vadim 7 Ren, Guojing 7 Sun, Yuangong 7 Tuna, Hüseyin 7 Wang, Youyu 7 Zheng, Zhaowen 6 Erbe, Lynn Harry 6 Klaus, Martin 6 Krall, Allan M. 6 Littlejohn, Lance L. 6 Pedersen, Steen 6 Teschl, Gerald 6 Wong, James S. W. 5 Aliyev, Ziyatkhan S. 5 Binding, Paul Anthony 5 Brown, Richard Clark 5 Browne, Patrick J. 5 Hooker, John W. 5 Kaymakçalan, Billur 5 Mingarelli, Angelo B. 5 Mukhtarov, Oktay Sh. 5 Peterson, Allan C. 5 Remling, Christian 5 Saker, Samir H. 5 Schulz-Baldes, Hermann 5 Simon, Barry 5 Sun, Shurong 5 Tharwat, Mohammed M. 5 Weikard, Rudi 5 Xie, Bing 5 Zhang, Meirong 5 Zhang, Qiming 4 Bohner, Martin J. 4 Brown, B. Malcolm 4 Clark, Steve 4 de Snoo, Hendrik S. V. 4 Dhar, Sougata 4 Fiedler, Frank 4 Frentzen, Hilbert 4 Jørgensen, Palle E. T. 4 Kaper, Hans G. 4 Kauffman, Robert M. 4 Kirane, Mokhtar 4 Kong, Qingkai 4 Li, Kun 4 Patula, William T. 4 Read, Thomas T. 4 Rybkin, Alexei 4 Šepitka, Peter 4 Simonov, Sergey A. 4 Tang, Xianhua 4 Tian, Feng 4 Watson, Bruce Alastair 3 Al-Hammadi, Abdulaziz Sultan Ali 3 Almenar, Pedro 3 Atia, Hany A. 3 Atkinson, Frederick Valentine 3 Bairamov, Elgiz 3 Belinsky, Boris P. 3 Çakmak, Devrim 3 Chlebicka, Iwona 3 Chua, Seng-Kee 3 Clemence, Dominic P. 3 Eastham, Michael S. P. 3 Eckhardt, Jonathan 3 Ghatasheh, Ahmed 3 Hao, Xiaoling 3 Harris, Bernard J. 3 Hasil, Petr 3 Helton, Jon C. 3 Ji, Shuguan 3 Jódar Sanchez, Lucas Antonio ...and 495 more Authors
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### Cited in 170 Serials

 79 Journal of Mathematical Analysis and Applications 54 Journal of Differential Equations 48 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 31 Applied Mathematics and Computation 28 Proceedings of the American Mathematical Society 22 Mathematische Nachrichten 19 Journal of Computational and Applied Mathematics 17 Computers & Mathematics with Applications 17 Journal of Mathematical Physics 17 Journal of Difference Equations and Applications 13 Linear Algebra and its Applications 12 Applicable Analysis 12 Transactions of the American Mathematical Society 11 Rocky Mountain Journal of Mathematics 10 Applied Mathematics Letters 10 Abstract and Applied Analysis 10 Advances in Difference Equations 9 Journal of Functional Analysis 9 Boundary Value Problems 8 Integral Equations and Operator Theory 8 Journal of Approximation Theory 8 Quaestiones Mathematicae 8 Journal of Inequalities and Applications 6 Mathematica Slovaca 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Communications in Mathematical Physics 5 Czechoslovak Mathematical Journal 5 Mathematische Zeitschrift 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Journal of Function Spaces 4 Journal d’Analyse Mathématique 4 Mathematical Methods in the Applied Sciences 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Mathematical and Computer Modelling 4 Discrete Dynamics in Nature and Society 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Mathematical Notes 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Advances in Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Mathematika 3 Filomat 3 Fractional Calculus & Applied Analysis 3 Complex Analysis and Operator Theory 3 Operators and Matrices 3 Journal of Mathematical Inequalities 3 Journal of Nonlinear Science and Applications 3 Differential Equations and Applications 2 Letters in Mathematical Physics 2 Reports on Mathematical Physics 2 Ukrainian Mathematical Journal 2 Journal of Optimization Theory and Applications 2 Journal of Soviet Mathematics 2 Manuscripta Mathematica 2 Monatshefte für Mathematik 2 Zeitschrift für Analysis und ihre Anwendungen 2 Acta Applicandae Mathematicae 2 Numerical Algorithms 2 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 2 Acta Mathematica Sinica. New Series 2 Journal of Dynamics and Differential Equations 2 Russian Journal of Mathematical Physics 2 Turkish Journal of Mathematics 2 Differential Equations and Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Novi Sad Journal of Mathematics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Acta Mathematica Sinica. English Series 2 Annales Henri Poincaré 2 Discrete and Continuous Dynamical Systems. Series B 2 Central European Journal of Mathematics 2 Journal of Spectral Theory 2 ISRN Mathematical Analysis 2 Analysis and Mathematical Physics 2 Nonlinear Analysis. Theory, Methods & Applications 2 Vestnik KRAUNTS. Fiziko-Matematicheskie Nauki 1 Archive for History of Exact Sciences 1 Archive for Rational Mechanics and Analysis 1 General Relativity and Gravitation 1 Indian Journal of Pure & Applied Mathematics 1 Israel Journal of Mathematics 1 Nonlinearity 1 Arkiv för Matematik 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 Journal of Geometry and Physics 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Annales de l’Institut Fourier 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 The Arabian Journal for Science and Engineering 1 Archiv der Mathematik 1 Automatica 1 Calcolo 1 Colloquium Mathematicum 1 Dissertationes Mathematicae 1 Duke Mathematical Journal 1 Glasgow Mathematical Journal 1 Journal of Applied Probability 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Statistical Planning and Inference ...and 70 more Serials
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### Cited in 40 Fields

 506 Ordinary differential equations (34-XX) 189 Operator theory (47-XX) 109 Difference and functional equations (39-XX) 73 Partial differential equations (35-XX) 65 Real functions (26-XX) 50 Dynamical systems and ergodic theory (37-XX) 38 Quantum theory (81-XX) 23 Numerical analysis (65-XX) 21 Special functions (33-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 21 Functional analysis (46-XX) 11 Integral equations (45-XX) 9 Mechanics of deformable solids (74-XX) 8 Systems theory; control (93-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Information and communication theory, circuits (94-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Functions of a complex variable (30-XX) 5 Probability theory and stochastic processes (60-XX) 5 Mechanics of particles and systems (70-XX) 5 Fluid mechanics (76-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Approximations and expansions (41-XX) 3 Relativity and gravitational theory (83-XX) 3 Biology and other natural sciences (92-XX) 2 Combinatorics (05-XX) 2 Potential theory (31-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX)