Edward J. McShane | Academic Influence

Edward J. McShane's AcademicInfluence.com Rankings

Edward J. McShane

Mathematics

#3500

Historical Rank

Real Analysis

#13

Historical Rank

Measure Theory

#967

Historical Rank

mathematics Degrees

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Mathematics

Edward J. McShane's Degrees

PhD Mathematics University of Chicago
Masters Mathematics University of Chicago
Bachelors Mathematics University of Notre Dame

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Why Is Edward J. McShane Influential?

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According to Wikipedia, Edward James McShane was an American mathematician noted for his advancements of the calculus of variations, integration theory, stochastic calculus, and exterior ballistics. His name is associated with the McShane–Whitney extension theorem and McShane integral. McShane was professor of mathematics at the University of Virginia, president of the American Mathematical Society, president of the Mathematical Association of America, a member of the National Science Board and a member of both the National Academy of Sciences and the American Philosophical Society.

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Edward J. McShane'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

Extension of range of functions (1934) (543)
Stochastic Calculus and Stochastic Models (1974) (203)
Relaxed Controls and Variational Problems (1967) (86)
On Filippov’s implicit functions lemma (1967) (83)
Stochastic Differential Equations and Models of Random Processes (1972) (80)
On Multipliers for Lagrange Problems (1939) (67)
Jensen's inequality (1937) (67)
Order-Preserving Maps and Integration Processes. (1954) (66)
The Lagrange Multiplier Rule (1973) (57)
A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals (1971) (55)
Linear functionals on certain Banach spaces (1950) (49)
The calculus of variations from the beginning through optimal control theory (1989) (47)
Necessary conditions in generalized-curve problems of the calculus of variations (1940) (40)
A Unified Theory of Integration (1973) (38)
A theorem on quadratic forms and its application in the calculus of variations (1940) (35)
Images of Sets Satisfying the Condition of Baire (1950) (34)
Parametrizations of saddle surfaces, with application to the problem of plateau (1933) (34)
Partial Orderings and Moore-Smith Limits (1952) (30)
Sufficient conditions for a weak relative minimum in the problem of Bolza (1942) (30)
Stochastic differential equations (1975) (28)
Stochastic Integrals and Stochastic Functional Equations (1969) (24)
Existence theorems for Bolza problems in the calculus of variations (1940) (21)
Families of measures and representations of algebras of operators (1962) (18)
Integrals Over Surfaces in Parametric Form (1933) (18)
On the solutions of the differential equation $y\sp”+p\sp{2}y=0$ (1966) (18)
ON THE SOLUTIONS OF LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS. (1965) (17)
On the Semi-Continuity of Double Integrals in the Calculus of Variations (1932) (16)
Integrals devised for special purposes (1963) (15)
Remark Concerning Integration. (1949) (14)
On the Necessary Condition of Weierstrass in the Multiple Integral Problem of the Calculus of Variations. II (1931) (13)
Existence theorems for ordinary problems of the calculus of variations (part I) (1934) (13)
V – Stochastic Differential Equations (1974) (11)
Order-Preserving Maps and Integration Processes. (AM-31) (1954) (11)
On the Second Variation in Certain Anormal Problems of the Calculus of Variations (1941) (11)
A Navigation Problem in the Calculus of Variations (1937) (9)
Differential and Integral Calculus: Courant/Differential (1988) (8)
Curve-space topologies associated with variational problems (1940) (8)
Toward a stochastic calculus, ii. (1969) (8)
Some existence theorems for problems in the calculus of variations (1938) (7)
On Perron integration (1942) (6)
Toward a stochastic calculus, I. (1969) (6)
On the uniqueness of the solutions of differential equations (1939) (6)
On the Solutions of the Differential Equation y + p 2 y = 0 (1966) (6)
Existence theorems for double integral problems of the calculus of variations (1935) (6)
Some existence theorems in the calculus of variations. III. Existence theorems for nonregular problems (1939) (6)
AN ELEMENTARY TREATMENT OF THE MOTION OF A SPINNING PROJECTILE ABOUT ITS CENTER OF GRAVITY (1944) (6)
On the Analytic Nature of Surfaces of Least Area (1934) (5)
The Du Bois-Reymond relation in the calculus of variations (1934) (5)
A METRIC IN THE SPACE OF GENERALIZED CURVES (1950) (5)
Addenda and corrigenda to “On Filippov’s implicit functions lemma”. (1969) (4)
A dominated-convergence theorem (1955) (4)
Some existence theorems in the calculus of variations. I. The Dresden corner condition (1938) (4)
On the necessary condition of Weierstrass in the multiple integral problem of the calculus of variations III (1967) (4)
Semi-continuity of integrals in the calculus of variations (1936) (4)
The choice of a stochastic model for a noise system (1976) (3)
A modified Riemann-Stieltjes integral (1952) (3)
The deterministic Itô-belated integral is equivalent to the Lebesgue integral (1978) (3)
Invariant extensions of linear functionals, with applications to measures and stochastic processes (1969) (3)
Some existence theorems in the calculus of variations. II. Existence theorems for isoperimetric problems in the plane (1938) (2)
A remark concerning sufficiency theorems for the problem of Bolza (1940) (2)
Some existence theorems in the calculus of variations. IV. Isoperimetric problems in non-parametric form (1939) (2)
The Radius of Gyration of a Convex Body (1962) (2)
Award for Distinguished Service to Professor William Larkin Duren, Jr. (1967) (2)
Review: Tibor Radó, Length and area (1948) (1)
The radius of gryration of a convex body (1962) (1)
WEAK TOPOLOGIES FOR STOCHASTIC PROCESSES. (1962) (1)
A GENERALIZATION OF CONVEXITY, AND MARTINGALES IN LINEAR SPACES. (1965) (1)
An Interpolation Formula (1946) (1)
Integration in linear spaces (1965) (1)
On the minimizing property of the harmonic function (1934) (1)
MAA Studies in Mathematics, Volume 1, Studies in Modern Analysis. (1962) (1)
On the Osgood-Carathéodory Theorem (1937) (1)
Concerning the semi-continuity of ordinary integrals of the calculus of variations (1934) (0)
Equations in Canonical Form (1974) (0)
The differentials of certain functionals in exterior ballistics (1950) (0)
A remark concerning the necessary condition of Weierstrass (1931) (0)
Trends in Analysis (1967) (0)
Chapter IX. Differential Equations (1961) (0)
Real analysis / Edward James McShane, Truman Arthur Botts (1959) (0)
Existence of Stochastic Integrals (1974) (0)
Chapter V. Differentiation (1961) (0)
On a Class of Alternating Cyclic Convolutional Codes (1975) (0)
CHAPTER I. PARTIALLY ORDERED SETS AND SYSTEMS (1954) (0)
Discussions: An Application of Fourier Series and a Theorem on Definite Integrals (1926) (0)
The Fourier Transform and Mean Convergence (1961) (0)
Chapter III. Measurable Sets and Measurable Functions (1961) (0)
Award for Distinguished Service to Professor Leon Walter Cohen (1976) (0)
Computation of Flat Trajectories with High Angles of Departure (1941) (0)
CHAPTER VI. APPLICATIONS (1954) (0)
Continuity, Chain Rule, and Substitution (1974) (0)
Corrections of Elements of Bombing Tables for Effects of Height of Target (1943) (0)
The Jacobi condition and the index theorem in the calculus of variations (1939) (0)
Discussions: The Error in an Approximate Division of the Circle (1927) (0)
Chapter VIII. The Perron Integral (1961) (0)
II – Stochastic Integrals (1974) (0)
Chapter VI. Continuity Properties of Measurable Functions (1961) (0)
Chapter II. The Lebesgue Integral (1961) (0)
Chapter X. Differentiation of Multiple Integrals (1961) (0)
Chapter VII. The Lebesgue-Stieltjes Integral (1961) (0)
The Addition Formulas for the Sine and Cosine (1941) (0)
CHAPTER III. LATTICE PROPERTIES, CONVERGENCE AND MEASURABILITY (1954) (0)
Chapter IV. The Integral as a Function of Sets; Convergence Theorems (1961) (0)
Chapter I. Some Theorems on Real-valued Functions (1961) (0)
A canonical form for antiderivatives (1959) (0)
CHAPTER II. DEFINITION OF THE MAPPING (1954) (0)
CHAPTER V. REAL-VALUED FUNCTIONS (1954) (0)
CHAPTER IV. ALGEBRAIC OPERATIONS (1954) (0)
On Stieltjes integration (1956) (0)

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