Wilhelmus Luxemburg

Wilhelmus Luxemburg's AcademicInfluence.com Rankings

Wilhelmus Luxemburg

Mathematics

#1711

World Rank

#2744

Historical Rank

#700

USA Rank

Measure Theory

#1415

World Rank

#1776

Historical Rank

#489

USA Rank

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Mathematics

Why Is Wilhelmus Luxemburg Influential?

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According to Wikipedia, Wilhelmus Anthonius Josephus Luxemburg was a Dutch American mathematician who was a professor of mathematics at the California Institute of Technology. He received his B.A. from the University of Leiden in 1950; his M.A., in 1953; his Ph.D., from the Delft Institute of Technology, in 1955. He was assistant professor at Caltech during 1958–60; Associate Professor, during 1960–62; Professor, during 1962–2000; Professor Emeritus, from 2000. He was the Executive Officer for Mathematics during 1970–85. In 2012 he became a fellow of the American Mathematical Society. Luxemburg became a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1974.

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Wilhelmus Luxemburg'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

Non-Standard Analysis (1977) (714)
Banach function spaces (1955) (390)
Introduction to the theory of infinitesimals (1976) (378)
Applications of model theory to algebra, analysis, and probability (1971) (173)
Notes on banach function spaces, I (1963) (148)
North-Holland Mathematical Library (2005) (130)
On the convergence of successive approximations in the theory of ordinary differential equations, II (1958) (73)
Compactness of integral operators in Banach function spaces (1963) (70)
A Radon-Nikodym type theorem for positive operators and a dual (1978) (66)
Some aspects of the theory of Riesz spaces (1979) (54)
Entire functions and Müntz-Szász type approximation (1971) (51)
Numerical methods and existence theorems for ordinary differential equations (1960) (48)
On the Convergence of Successive Approximations in the Theory of Ordinary Differential Equations (1958) (47)
What Is Nonstandard Analysis (1973) (47)
Some examples of normed Köthe spaces (1966) (42)
Non-Standard Analysis: Lectures on A. Robinson's Theory of Infinitesimals and Infinitely Large Numbers (1966) (39)
The linear modulus of an order bounded linear transformation. II (1971) (35)
Notes on Banach Function Spaces, XIVa (1965) (33)
On a class of valuation fields introduced by A. Robinson (1976) (30)
Some Remarks on Banach Function Spaces (1956) (29)
Conjugate Spaces of Orlicz Spaces (1956) (29)
An Extension theorem for Riesz homomorphisms (1979) (28)
Archimedean quotient Riesz spaces (1967) (26)
Two applications of the method of construction by ultrapowers to analysis (1962) (26)
Notes on Banach Function Spaces, VIII (1964) (25)
Arzelà's Dominated Convergence Theorem for the Riemann Integral (1971) (24)
Almost commuting matrices are near commuting matrices (1970) (23)
Multiplicativity factors for seminorms. II (1990) (23)
Positive Operators, Riesz Spaces, and Economics (1991) (22)
Notes on banach function spaces, V (1963) (21)
Positive Operators and Semigroups on Banach Lattices (1992) (19)
Notes on banach function spaces, II (1963) (19)
On the measurability of a function which occurs in a paper by A.C. Zaanen (1958) (18)
An Extension of the Concept of the Order Dual of a Riesz Space (1967) (18)
Notes on banach function spaces VI (1963) (16)
Notes on Banach Function Spaces, X (1964) (15)
Notes on banach function spaces, VII (1963) (14)
Contributions to Non-Standard Analysis (1972) (14)
Notes on banach function spaces. IV (1963) (14)
Notes on Banach Function Spaces, XVa (1965) (14)
On an asymptotic problem concerning the laplace transform (1978) (13)
Notes on Banach Function Spaces, IX (1964) (12)
Notes on Banach Function Spaces, XI (1964) (12)
A remark on Sikorski's extension theorem for homomorphisms in the theory of Boolean algebras (1964) (12)
Operator Theory in Function Spaces and Banach Lattices: Essays Dedicated To A.C. Zaanen On The Occasion Of His 80Th Birthday (2011) (10)
Notes on Banach Function Spaces, XVIa (1965) (10)
Notes on Banach Function Spaces, XIII (1964) (10)
Maharam extensions of positive operators and f-modules (2002) (10)
Notes on banach function spaces. III (1963) (10)
Multiplicativity Factors for Orlicz Space Function Norms (1993) (9)
Integration with Respect to Finitely Additive Measures (1991) (9)
The Existence of Non-Trivial Bounded Functionals Implies the Hahn-Banach Extension Theorem (2001) (9)
Advances in Analysis, Probability and Mathematical Physics: Contributions of Nonstandard Analysis (1995) (8)
Addendum to “on the measurability of a function which occurs in a paper by A. C. Zaanen” (1963) (8)
Notes on Banach Function Spaces, XII (1964) (8)
Is every integral normal (1967) (7)
On Some Concurrent Binary Relations Occurring in Analysis (1972) (7)
Notes on Banach Function Spaces, XVb (1965) (7)
Notes on Banach Function Spaces XIVb (1965) (7)
An alternative proof of a Radon-Nikodym theorem for lattice homomorphisms (1992) (6)
Positive operators, Riesz spaces, and economics : proceedings of a conference at Caltech, Pasadena, California, April 16-20, 1990 (1991) (6)
Discontinuous subnorms (2001) (6)
The Work of Dorothy Maharam on Kernel Representations of Linear Operators (1989) (6)
Stable Subnorms II (2003) (6)
On an Inequality of A. Khintchine for Zero-One Matrices (1972) (6)
Multiplicativity Factors for Function Norms (1993) (6)
The abstract riemann integral and a theorem of G. Fichtenholz on equality of repeated riemann integrals. Ib (1961) (6)
On Finitely Additive Measures in Boolean Algebras. (1964) (6)
Representations of Positive Projections II (2005) (6)
A Nonstandard Analysis Approach to Fourier Analysis (1972) (5)
On the existence of-complete prime ideals in Boolean algebras (1968) (5)
A Remark on a Paper by N. G. De Bruijn and P. Erdös (1962) (5)
Extensions of prime ideals and the existence of projections in Riesz spaces (1973) (5)
Notes on Banach Function Spaces XVIb (1965) (5)
ON THE IDEAL STRUCTURE OF POSITIVE , EVENTUALLY COMPACT LINEAR OPERATORS ON BANACH LATTICES (2012) (4)
From A to Z : proceedings of a symposium in honour of A. C. Zaanen [held at Leiden, 05-06.07.1982] (1982) (4)
Reflexivity of the length function (1957) (4)
Stable subnorms revisited (2004) (4)
Ordered Algebraic Structures in Analysis (1989) (4)
A note on the sum of two closed linear subspaces (1985) (4)
Advances in Analysis, Probability and Mathematical Physics (1995) (3)
A Remark on the Cantor-Lebesgue Lemma (1972) (3)
Diagonals of the Powers of an Operator on a Banach Lattice (1995) (3)
Addendum to "The Abstract Riemann Integral and a Theorem of G. Fichtenholz on Equality of Repeated Riemann Integrals Ia and Ib" (1962) (3)
Stable seminorms revisited (1998) (3)
Representations of Positive Projections I (2005) (2)
On an inequality of Levinson of the Phragmèn-Lindelöf type (1984) (2)
Stable Norms on Complex Numbers and Quaternions (1999) (2)
Allendoerfer Advanced Series: Measure and Integration . Sterling K. Berberian. Macmillan, New York, 1965. xx + 312 pp. Illus. $9.95. (1965) (2)
Not all quadrative norms are strongly stable (2001) (2)
On some order properties of Riesz spaces and their relations (1968) (2)
Analysis and geometry : trends in research and teaching (1992) (2)
Sundual characterizations of the translation group of R (2002) (2)
MathematicsAn extension theorem for Riesz homomorphisms (1979) (2)
On the spectra of certain Laurent operators on Orlicz spaces $l^{Φ}$ (1968) (2)
Advanced Problems: 5707-5713 (1970) (1)
On an infinite series of Abel occurring in the theory of interpolation (1975) (1)
Positive Operators and Semigroups on Banach Lattices : Proceedings of a Caribbean Mathematics Foundation Conference 1990 (1992) (1)
Problems for Solution: 5025-5030 (1962) (1)
Review: Jens Erik Fenstad, A Note on Standard versus Non-Standard Topology (1970) (1)
Contributions to Functional Analysis (1966) (1)
Notes on the Theory of Integration : Ma 108 (1960) (1)
Curriculum Vitae of A.C. Zaanen (1995) (0)
Limit of an Integral (1969) (0)
The Stieltjes Integral, the Concept that Transformed Analysis (1993) (0)
General Theory of Banach Algebras . Charles E. Rickart Van Nostrand, New York, 1960. 405 pp. $10.50. (1961) (0)
Characterizations of Sunduals (Summary) (2003) (0)
Advanced Problems: 5430-5439 (1966) (0)
Problems for Solution: 5019-5024 (1962) (0)
The weak closure of the equimeasurable rearrangements of a measurable function by Peter W. Day* (2004) (0)
A remark on R. R. PHELPS' paper “subreflexive normed linear spaces” (1960) (0)
Near-standard compact internal linear operators (2020) (0)
Maharam extensions of positive operators and <Emphasis Type="Italic">f</Emphasis>-modules (2002) (0)
AMERICAN MATHElfaATICAL SOCIETY (1977) (0)
A Property of the Fourier Coefficients of an Integrable Function (1962) (0)
List of Publications of A.C. Zaanen (1995) (0)
Introduction of the methods of real analysis, by Maurice Sion. Holt, Rinehart and Winston Inc., New York, 1968. x + 134 pages. Canad. $9.85. (1969) (0)
Algebraic Theory of Measure and Integration, by C. Carathéodory. Chelsea Publishing Company, New York, N. Y., 1963. 378 pages. (1964) (0)
A Distributional proof of a theorem of Plessner (2009) (0)
A Factorial Polynomial Inequality (A. Fransén) (1984) (0)
Fenstad Jens Erik. A note on “standard” versus “non-standard” topology. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings , series A, vol. 70 (1967), pp. 378–380; also Indagationes mathematicae, vol. 29 (1967), pp. 378–380. (1970) (0)
Robinson’s Nonstandard Analysis and its Influence on Mathematics (1990) (0)
Robinson, Abraham (1918–1974) (1987) (0)
Closure properties of sequences of exponentals { exp (i λn t) } (1974) (0)
Program Analysis Symposium on the occasion of the 80th birthday of A.C. Zaanen (1995) (0)
General Theory of Banach Algebras. Charles E. Rickart Van Nostrand, New York, 1960. 405 pp. $10.50 (1961) (0)
Interview with W. A. J. Luxemburg (2001) (0)

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