# Paul Butzer

Paul Leo Butzer (born 15 April 1928) is a German mathematician who specializes in Analysis (Approximation theory, Harmonic analysis).

## Life and work

Butzer was born in Mülheim an der Ruhr on 15 April 1928. He is the son of an engineer, and his mother studied mathematics at RWTH Aachen University. As opponents of the National Socialists (Nazis), Butzer's parents left Germany with their children in 1937 and moved to England. During World War II, they relocated to Canada, where Butzer attended school in Montreal and studied mathematics at Loyola College (later Concordia University), completing his bachelor's degree in 1948. He then pursued further studies at the University of Toronto, including studying under Harold Scott MacDonald Coxeter and William Tutte, and obtained his Ph.D. in 1951 under the supervision of George G. Lorentz (On Bernstein polynomials). In 1952, he became a lecturer and then an assistant professor at McGill University. In 1955/56, he lived in Paris and then in Mainz. He decided to stay in Germany, where he completed his habilitation at the University of Freiburg, taught in Würzburg, and starting in 1958, at RWTH Aachen University. In 1962, he was appointed professor there. In 1963, he began organizing international conferences on Approximation theory at the Oberwolfach Research Institute for Mathematics, later together with Béla Szőkefalvi-Nagy.
In addition to approximation theory and its connections to Fourier analysis and semigroups of operators in Banach spaces, Butzer also worked on probability theory (Central limit theorem and related Convergence tests issues), Sampling Theory, and Signal analysis.
Paul Leo Butzer also delved into the history of mathematics, particularly in its connection with Aachen. He studied figures such as Peter Gustav Lejeune Dirichlet, Eduard Helly, Eugène Catalan, Pafnuty Chebyshev, Charles Jean de la Vallée Poussin, the history of splines, Otto Blumenthal, mathematics in the Carolingian era, and Elwin Bruno Christoffel (on whom he published a book).
Butzer is a member of the Royal Society of Sciences in Liège and the Royal Belgian Academy of Sciences. He is an honorary member of the Mathematical Society in Hamburg. He has received honorary doctorates from three universities: Liège, York, and Timișoara.
Paul Butzer is the brother of Karl W. Butzer.

## Publications

* With Hubert Berens: "Semi-groups of Operators and Approximation," Grundlehren der mathematischen Wissenschaften, Springer Verlag, 1967.
* With Hermann Schulte: "Ein Operatorenkalkül zur Lösung gewöhnlicher und partieller Differenzengleichungssysteme von Funktionen diskreter Veränderlicher und seine Anwendungen," Köln, Opladen, Westdeutscher Verlag, 1965.
* With Rolf Joachim Nessel: "Fourier Analysis and Approximation," Academic Press, Vol. 1 (One-dimensional Theory), 1971.
* With Walter Trebels: "Hilberttransformation, gebrochene Integration und Differentiation," Köln, Opladen, Westdeutscher Verlag, 1968.
* With Karl Scherer: "Approximationsprozesse und Intepolationsmethoden," BI Hochschultaschenbuch, Mannheim, 1968.
* With W. Oberdörster: "Darstellungssätze für beschränkte lineare Funktionale im Zusammenhang mit Hausdorff-, Stieltjes- und Hamburger-Momentenproblemen," Opladen, Westdeutscher Verlag, 1975.
* Edited with Dietrich Lohrmann: "Science in Western and Eastern Civilization in Carolingian Times," Birkhäuser, 1993.
* Edited with Walter Oberschelp and Max Kerner: "Karl der Grosse und sein Nachwirken: 1200 Jahre Kultur und Wissenschaft in Europa," 2 volumes, Turnhout, Brepols, 1997/98.
* "Mathematics in West and East from the fifth to tenth centuries: an overview," in P. L. Butzer, Dietrich Lohrmann (Eds.): "Science in Western and Eastern civilization in Carolingian times," Basel, 1993, pp. 443–481.
* With Karl W. Butzer: "Mathematics at Charlemagne's court and its transmission," in Catherine Cubitt (Ed.): "Court culture in the early middle ages," Turnhout, 2003, pp. 77–89.
* "The Mathematicians of the Aachen-Liège Region from the Carolingian to the Late Ottonian Period" (Die Mathematiker des Aachen-Lütticher Raumes von der karolingischen bis zur spätottonischen Epoche), in Annalen des Historischen Vereins für den Niederrhein, Volume 178, 1976, pp. 7–30.
* Edited with F. Féher: "E. B. Christoffel, the influence of his work on mathematics and the physical sciences," Birkhäuser, 1981.
* With Francois Jongmans: "P. L. Chebyshev (1821–1894): a guide to his life and work," Lehrstuhl für Mathematik A, RWTH Aachen, 1998.
* "Dirichlet and his role in the founding of mathematical physics," Lehrstuhl A für Mathematik, RWTH Aachen, 1983.