Philip Hartman

Q: What Schools Are Affiliated With Philip Hartman

Philip Hartman is affiliated with the following schools: Queens College, City University of New York, Princeton University, Stanford University, Johns Hopkins University

Philip Hartman's AcademicInfluence.com Rankings

Philip Hartman

Mathematics

#760

World Rank

#1376

Historical Rank

#332

USA Rank

Measure Theory

#69

World Rank

#112

Historical Rank

#38

USA Rank

mathematics Degrees

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Mathematics

Philip Hartman's Degrees

PhD Mathematics Princeton University
Masters Mathematics Stanford University

Why Is Philip Hartman Influential?

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According to Wikipedia, Philip Hartman was an American mathematician at Johns Hopkins University working on differential equations who introduced the Hartman–Grobman theorem. He served as Chairman of the Mathematics Department at Johns Hopkins for several years. He has an Erdös number of 2.

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Philip Hartman's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Ordinary Differential Equations (1965) (8180)
On some non-linear elliptic differential-functional equations (1966) (906)
A lemma in the theory of structural stability of differential equations (1960) (306)
On Spherical Image Maps Whose Jacobians Do Not Change Sign (1959) (277)
On Homotopic Harmonic Maps (1967) (267)
On the Law of the Iterated Logarithm (1941) (248)
On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations (1953) (240)
On functions representable as a difference of convex functions (1959) (234)
Difference equations: disconjugacy, principal solutions, Green’s functions, complete monotonicity (1978) (189)
On the local linearization of differential equations (1963) (159)
On completely continuous Hankel matrices (1958) (148)
ON AN ORDINARY DIFFERENTIAL EQUATION (2010) (144)
GEODESIC PARALLEL COORDINATES IN THE LARGE. (1964) (135)
Self-adjoint, non-oscillatory systems of ordinary, second order, linear differential equations (1957) (128)
THE SPECTRA OF TOEPLITZ'S MATRICES.* (1950) (124)
On boundary value problems for systems of ordinary, nonlinear, second order differential equations (1960) (117)
On Non-Oscillatory Linear Differential Equations of Second Order (1952) (117)
On nonoscillatory linear differential equations of second order (1977) (116)
Asymptotic Integrations of Linear Differential Equations (1955) (108)
Ordinary differential equations, Second Edition (2002) (106)
"Normal" Distribution Functions on Spheres and the Modified Bessel Functions (1974) (105)
ON HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS. (1952) (98)
On solutions of the Helmholtz equation in exterior domains (1961) (89)
On Stability in the Large for Systems of Ordinary Differential Equations (1961) (88)
Umbilical Points and W-Surfaces (1954) (86)
On the Infinitesimal Generators of Integral Convolutions (1942) (82)
On global asymptotic stability of solutions of differential equations. (1962) (80)
On the isometric immersions in Euclidean space of manifolds with nonnegative sectional curvatures. II (1965) (78)
On the smoothness of isometries (1970) (71)
On $N$-parameter families and interpolation problems for nonlinear ordinary differential equations (1971) (69)
Differential equations with non-oscillatory eigenfunctions (1948) (66)
On boundary value problems for superlinear second order differential equations (1977) (65)
On an Oscillation Criterion of Liapounoff (1951) (64)
Linear Differential and Difference Equations with Monotone Solutions (1953) (63)
ON THE ASYMPTOTIC CURVES OF A SURFACE. (1951) (54)
Unrestrictedn-parameter families (1958) (52)
ON THE THIRD FUNDAMENTAL FORM OF A SURFACE. (1953) (50)
On the Fundamental Equations of Differential Geometry (1950) (49)
On invariant sets and on a theorem of Ważewski (1972) (48)
PRINCIPAL SOLUTIONS OF DISCONJUGATE n-TH ORDER LINEAR DIFFERENTIAL EQUATIONS. (1969) (43)
On the Local Uniqueness of Geodesics (1950) (42)
On Dirichlet Series Involving Random Coefficients (1939) (40)
On complete hypersurfaces of nonnegative sectional curvatures and constant th mean curvature (1978) (38)
On isometries and on a theorem of Liouville (1958) (38)
On a comparison theorem for selfadjoint partial differential equations of elliptic type (1955) (37)
Oscillation criteria for self-adjoint second-order differential systems and “principal sectional curvatures” (1979) (36)
On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations: III. Approximations by Spherical Harmonics (1955) (35)
The divergence of non-harmonic gap series (1942) (34)
On the Non-Increasing Solutions of y = f(x,y,y ) (1951) (33)
ON THE BOUNDED SLOPE CONDITION (1966) (32)
THE NUMBER OF L2-SOLUTIONS OF x" + q(t)x 0.* (1951) (32)
An Oscillation Theorem for Continuous Spectra. (1947) (32)
On the Solutions of the Equation of Heat Conduction (1950) (30)
Completely monotone families of solutions of $n$-th order linear differential equations and infinitely divisible distributions (1976) (30)
A Criterion for the Non-Degeneracy of the Wave Equation (1949) (30)
On Uniform Dini Conditions in the Theory of Linear Partial Differential Equations of Elliptic Type (1955) (28)
A Characterization of the Spectra of One-Dimensional Wave Equations (1949) (28)
On the asymptotic integration of ordinary differential equations (1963) (27)
The existence of large or small solutions of linear differential equations (1961) (26)
On Disconjugate Differential Systems (1956) (26)
Unrestricted solution fields of almost-separable differential equations (1948) (25)
GAUSSIAN CURVATURE AND LOCAL EMBEDDING. (1951) (25)
ON DISCONJUGACY CRITERIA (1970) (24)
Asymptotic Integrations of Ordinary Non-Linear Differential Equations (1955) (24)
On Sine Series with Monotone Coefficients (1953) (23)
The Least Cluster Point of the Spectrum of Boundary Value Problems (1948) (23)
On the Spherical Approach to the Normal Distribution Law (1940) (23)
On the Zeros of Solutions of Second Order Linear Differential Equations (1952) (23)
Criteria of Non-Degeneracy for the Wave Equation (1948) (23)
On the Asymptotic Behaviour of Solutions of a Differential Equation in Boundary Layer Theory (1964) (23)
On a Theorem of Milloux (1948) (22)
On the Existence of Similar Solutions of Some Boundary Layer Problems (1972) (22)
On the Embedding Problem in Differential Geometry (1950) (22)
A Separation Theorem for Continuous Spectra (1949) (21)
ON NON-OSCILLATORY LINEAR DIFFERENTIAL EQUATIONS.* (1953) (18)
On Geodesic Coordinates (1951) (18)
On Elliptic Partial Differential Equations and Uniqueness Theorems for Closed Surfaces (1958) (16)
On solutions of ΔV+V=0 in an exterior region (1959) (16)
Disconjugate $n$th order differential equations and principal solutions (1968) (16)
On the Linear Logarithmico-Exponential Differential Equation of the Second Order (1948) (16)
On an oscillation criterion of de la Valleé Poussin (1955) (15)
The Structure of Monotone Functions (1937) (15)
THE GAPS IN THE ESSENTIAL SPECTRA OF WAVE EQUATIONSA (1950) (15)
Normal Distributions and the Law of the Iterated Logarithm (1941) (15)
On Linear Second Order Differential Equations with Small Coefficients (1951) (15)
On the Products of Solutions of Second Order Disconjugate Differential Equations and the Whittaker Differential Equation (1977) (14)
On Monotone Solutions of Systems of Non-Linear Differential Equations (1954) (14)
Mean motions and almost periodic functions (1939) (14)
ON THE EXISTENCE OF RIEMANNIAN MANIFOLDS WHICH CANNOT CARRY NON-CONSTANT ANALYTIC OR HARMONIC FUNCTIONS IN THE SMALL.* (1953) (14)
On the Essential Spectra of Singular Eigenvalue Problems (1950) (13)
On Non-Conservative Linear Oscillators of Low Frequency (1948) (13)
On the Ergodic Theorems (1947) (13)
Systems of Total Differential Equations and Liouville's Theorem on Conformal Mappings (1947) (13)
Frobenius theorem under Carathéodory type conditions (1970) (12)
On Differential Equations and the Function $J_\{mu}^2 + Y_\{mu}^2$ (1961) (12)
On the Asymptotic Behavior of the Solutions of a Non-Linear Differential Equation (1946) (12)
On the Essential Spectra of Symmetric Operators in Hilbert Space (1953) (11)
On Two-Point Boundary Value Problems for Nonlinear Second Order Systems (1974) (11)
On Unsmooth Two-Dimensional Riemannian Metrics (1952) (11)
Oscillatory and Non-Oscillatory Linear Differential Equations (1949) (10)
Boundary value problems for second order, ordinary differential equations involving a parameter☆ (1972) (10)
Asymptotic Integration of Ordinary Differential Equations (1983) (10)
The Asymptotic Arcus Variation of Solutions of Real Linear Differential Equations of Second Order (1948) (10)
On the Curvatures of a Surface (1953) (10)
Tauber's Theorem and Absolute Constants (1947) (10)
On the Fourier-Stieltjes Transform of a Singular Function (1938) (9)
Convex functions and mean value inequalities (1972) (9)
Corrigendum and Addendum: Principal Solutions of Disconjugate n-th Order Linear Differential Equations (1971) (9)
Uniqueness of principal values, complete monotonicity of logarithmic derivatives of principal solutions, and oscillation theorems (1979) (9)
ON UNBOUNDED TOEPLITZ MATRICES.* 1 (1963) (9)
CONVEX SETS AND THE BOUNDED SLOPE CONDITION (1968) (9)
On the Singularities in Nets of Curves Defined by Differential Equations (1953) (9)
On a Class of Arithmetical Fourier Series (1938) (8)
On Linear Difference Equations of Second Order (1950) (8)
On the Spectra of Slightly Disturbed Linear Oscillators (1949) (8)
ON NON-OSCILLATORY LINEAR DIFFERENTIAL EQUATIONS WITH MONOTONE COEFFICIENTS.* (1954) (8)
Multiplicative sequences and Töplerian $(L^2)$-bases (1947) (8)
The swirling flow problem in boundary layer theory (1971) (8)
Remarks on a uniqueness theorem for closed surfaces (1957) (8)
On the Orientation of Unilateral Spectra (1948) (7)
ON THE LOCAL BEHAVIOR OF SOLUTIONS OF NON- PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. II. The Uniqueness of the Green Singularity.* (1954) (7)
On the Essential Spectra of Ordinary Differential Operators (1954) (7)
On the Location of Spectra of Wave Equations (1949) (7)
On a class of perturbations of the harmonic oscillator (1968) (7)
Errata: Asymptotic Integrations of Linear Differential Equations (1955) (7)
ON EXTERIOR DERIVATIVES AND SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS (1959) (7)
On the Laplace-Fourier Transcendents (1949) (6)
On Geodesic Torsions and Parabolic and Asymptotic Curves (1952) (6)
Hölder continuity and non-linear elliptic partial differential equations (1958) (6)
On Elliptic Monge-Ampere Equations (1953) (6)
On Mobius' Inversion (1947) (6)
On the Derivatives of the Solutions of One-Dimensional Wave Equations (1950) (6)
Separation Theorems for Bounded Hermitian Forms (1949) (6)
Mean Motions and Distribution Functions (1937) (6)
Perturbation of spectra and Krein extensions (1956) (6)
On the Distribution Functions of Almost Periodic Functions (1938) (6)
On Asymptotic Parametrizations (1953) (6)
Mean Value Theorems and Linear Operators (1955) (6)
Infinite convolutions on locally compact Abelian groups and additive functions (1975) (5)
The $L^2$-solutions of linear differential equations of second order (1947) (5)
On the Embedding of Hyperbolic Line Elements; A Correction (1952) (5)
Some Examples in the Theory of Singular Boundary Value Problems (1952) (5)
On disconjugate differential equations (1968) (5)
Generalized Lyapunov functions and functional equations (1965) (5)
Positive and monotone solutions of linear ordinary differential equations (1975) (5)
Linear Differential Equations with Completely Monotone Solutions (1954) (5)
On Pieces of Convex Surfaces (1953) (5)
Toplerian (L 2 )-Bases (1948) (5)
On Continuous Area-Preserving and Legendre Transformations (1954) (5)
Regular binary Pfaffians and non-parabolic partial differential equations (1954) (5)
ON THE LIMITS OF RIEMANN APPROXIMATING SUMS (1947) (5)
Integrability in the Large and Dynamical Stability (1943) (5)
Remarks on geodesics (1983) (4)
Disconjugacy and wronskians (1971) (4)
ON BOUNDED GREEN'S KERNELS FOR SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS.* (1951) (4)
Monotony Properties and Inequalities for Green’s Functions for Multipoint Boundary Value Problems (1978) (4)
On the Behavior of the Solutions of Real Binary Differential Systems at Singular Points (1953) (4)
On generalized ellipses (1959) (4)
On an ordinary differential equation involving a convex function (1969) (4)
On dichotomies for solutions ofn-th order linear differential equations (1962) (4)
A Differential Equation with Non-Unique Solutions (1963) (4)
ON THE LOCAL LINEARIZATION OF DIFFERENTIAL EQUATIONS1 (2010) (4)
ON THE EIGENVALUES OF DIFFERENTIAL EQUATIONS. (1951) (4)
On Perturbations of the Continuous Spectrum of the Harmonic Oscillator (1952) (4)
On maximum principles for non-hyperbolic partial differential operators (1957) (4)
On the Inverse of the Parabolic Differential Operator ∂ 2 /∂x 2 - ∂/∂t (1953) (3)
Lame Coordinates in Hilbert Space (1950) (3)
On the solutions of certain overdetermined systems of partial differential equations (1954) (3)
An inequality for the amplitudes and areas in vibration diagrams of time-dependent frequency (1952) (3)
'Normal' Distribution Functions on Spheres and the Modified Bessel Function (I Sub nu) (X). (1973) (3)
ON LINEAR AND NONLINEAR PERTURBATIONS OF LINEAR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS (1956) (3)
On the Asymptotic Problems of the Zeros in Wave Mechanics (1948) (3)
On linear, second order differential equations in the unit circle (1955) (3)
The existence and stability of stationary points (1966) (3)
The stable manifold of a point of a hyperbolic map of a Banach space (1971) (3)
On integrating factors and on conformal mappings (1958) (2)
Some Singular Nonoscillatory Boundary Value Problems (1979) (2)
Remark on Taylor's formula (1945) (2)
The (L)-Space of Relative Measure. (1947) (2)
On the behavior of Fourier sine transforms near the origin (1951) (2)
On the Standard Deviations of Additive Arithmetical Functions (1940) (2)
On solutions of disconjugate differential equations (1974) (2)
On oscillators with large frequencies. (1959) (2)
On Laurent operators on _ (1957) (2)
On Curves Defined by Binary Non-Conservative Differential Systems (1954) (2)
On third order, nonlinear, singular boundary value problems. (1971) (2)
An inequality for the first eigenvalue of an ordinary boundary value problem (1955) (2)
On smooth linear partial differential equations without solutions (1959) (2)
ON THE DERIVATIVES OF SOLUTIONS OF LINEAR, SECOND ORDER, ORDINARY DIFFERENTIAL EQUATIONS.* (1953) (2)
Asymptotic Distributions and the Ergodic Theorem (1939) (2)
On the maximum principles of A. D. Alexandrov in the uniqueness theory for hypersurfaces (1980) (2)
Integration of ordinary linear differential equations by Laplace-Stieltjes transforms (1975) (2)
Tplerian $(L\sp 2)$-bases (1948) (1)
Asymptotic Distributions and Statistical Independence (1939) (1)
Logarithmic derivatives of solutions of disconjugate differential equations (1974) (1)
An Asymptotic Formula for Exponential Integrals (1940) (1)
4. Linear Differential Equations (2002) (1)
On conformal maps defined by Lagrange’s series and by solutions ofdw/dz=f(w) (1954) (1)
9. Invariant Manifolds and Linearizations (2002) (1)
Integral Forms and Variational Orthogonality (1938) (1)
On Non-Linear Differential Equations of First Order (1950) (1)
Partial differential equations and a theorem of A. Kneser (1955) (1)
ON THE MAXIMA OF THE PATTERSON FUNCTIONS (1951) (1)
On the Almost Periodicity of Additive Number-Theoretical Functions (1940) (1)
Newtonian approximations to a zero of a function (1948) (1)
On the Solutions of an Ordinary Differential Equation Near a Singular Point (1946) (1)
On the Intuitive Approach to the Spectrum of a Wave Equation (1949) (1)
A Remark on a Theorem of Arzela (1937) (1)
Review: E. C. Titchmarsh, Eigenfunction expansions associated with second order differential equations, (1959) (1)
On the Classical Existence Theorem of Linear Differential Equations (1949) (1)
Statistical Independence and Statistical Equilibrium (1940) (1)
THE HARTMAN–GROBMAN THEOREM (2008) (1)
On the Effect of Decimal Corrections on Errors of Observation (1948) (1)
On the local behavior of solutions of Δ = g(x, u, ∇ u) (1956) (1)
The zeros of the derivatives of the real elliptic $\vartheta_3$-function (1948) (1)
III. Approximations by spherical harmonics. (2016) (1)
Additive functions and almost periodicity (1942) (1)
Interpolating families and generalized convex functions (1967) (1)
LP EMBEDDING AND NONLINEAR EIGENVALUE PROBLEMS FOR UNBOUNDED DOMAINS (2007) (0)
On the monotonicity of nonnegative solutions and the uniqueness of eigenvalues (1983) (0)
DEVIATIONS OF FOURIER SUMS ON CLASSES OF ENTIRE FUNCTIONS (1990) (0)
On a Problem of Poincare Concerning Riccati's Equation (1955) (0)
ON COMPLETE HYPERSURFACES OF NONNEGATTVE SECTIONAL CURVATURES AND CONSTANT mTH MEAN CURVATURE1 (2010) (0)
12. Use of Implicit Function and Fixed Point Theorems (2002) (0)
On certain monotone functions and products of independent functions (1961) (0)
14. Miscellany on Monotony (2002) (0)
On Upper Limit Relations for Number Theoretical Functions (1940) (0)
On Euler transforms (1950) (0)
10. Perturbed Linear Systems (2002) (0)
On the Classical Transcendents of Mathematical Physics (1951) (0)
Solutions of disconjugate third-order differential equations☆ (1977) (0)
11. Linear Second Order Equations (2002) (0)
ASYMPTOTICINTEGRATION OF ORDINARY DIFFERENTIALEQUATIONS (1983) (0)
3. Differential Inequalities and Uniqueness (2002) (0)
ON LOGARITHMIC DERIVATIVES OF SOLUTIONS OF DISCONJUGATE LINEAR nTH ORDER DIFFERENTIAL EQUATIONS (1972) (0)
13. Dichotomies for Solutions of Linear Equations (2002) (0)
INTEGRATION OF LINEAR DIFFERENTIAL EQUATIONS BY LAPLACE-STIELTJES TRANSFORMS (1975) (0)
The essential spectra belonging to bounded and half-bounded potentials (1956) (0)
On Jacobi Brackets (1957) (0)
On limits of Riemann sums and the range of integrals (1968) (0)
ON COMPLETELY CONTINUOUS HANKEL MATRICES1 (2010) (0)
8. Plane Stationary Points (2002) (0)
On the Sacksteder decomposition of complete W-hypersurfaces of nonnegative sectional curvature (1979) (0)
On the Convexity of Averages of Analytic Almost Periodic Functions (1941) (0)
ON GLOBAL ASYMPTOTIC STABILITY OF SOLUTIONS OF DIFFERENTIAL EQUATIONS ( 1 ) BY (2010) (0)
Binary, linear, elliptic, partial differential equations (1955) (0)
If a binary, symmetric, positive-definite matrix (gik) of functions (2016) (0)
The essential spectrum and averages of the potential (1956) (0)
7. The Poincaré-Bendixson Theory (2002) (0)
ON PARABOLIC CIJRVES ON SURFACES. (1954) (0)
ON TV-PARAMETER FAMILIES AND INTERPOLATION PROBLEMS FOR NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(1) (2010) (0)
Envelopes and Discriminant Curves (1953) (0)
Errata: On Linear Difference Equations of Second Order (1950) (0)
ON INTEGRATING FACTORS AND ON (2016) (0)
Errata: The Number of L 2 -Solutions of x = q(t)x = 0 (1951) (0)
5. Dependence on Initial Conditions and Parameters (2002) (0)
Letter from Philip E. Hartman to Joshua Lederberg (1952) (0)
ON THE ESSENTIAL SPECTRA OF SYMMETRIC OPERATORS (2016) (0)
6. Total and Partial Differential Equations (2002) (0)
Mathematical Techniques for the Analysis of the Dynamic Response of Flexible Vehicles. (1971) (0)

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What Schools Are Affiliated With Philip Hartman?

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