**Paul Butzer** is a German mathematician working in approximation theory and harmonic analysis.

- Once their parents were settled, Paul and Karl were able to join them and, by the autumn of 1937, Paul was studying at the Jesuit Wimbledon College.
- Butzer received an M.A. in 1949, being awarded the Sir Joseph Flavelle Prize the best performance.
- As this time Lorentz was writing his book Berstein polynomials so work in this area was a natural choice as a topic for Butzer.
- In 1951 Butzer was awarded a Ph.D. for his thesis On Bernstein Polynomials in which he studied classical Bernstein polynomials and their variant for integrable functions, namely Kantorovich polynomials.
- In 1962 he was offered a chair at Groningen, in the Netherlands, but this prompted RWTH to also offer Butzer a chair.
- Work in approximation theory continued, with topics such as best trigonometric approximation (extending the Jackson-Bernstein theory), and best approximation by algebraic polynomials, an area where some of Paul's finest results are to be found.
- Paul's interest in probability theory led him in another direction, beginning in about 1975, to study the central limit theorem and the rates associated with its basic convergence theorem.
- This problem was, of course, well-suited to Paul's expertise in approximation theory and Fourier analysis.
- Let us turn to Paul's involvement with signal theory, which began in about 1970 when he became interested in dyadic analysis, particularly the problem of defining a satisfactory derivative in that setting.
- A few years later, Paul's interests in the sampling theory of band-limited, and of not-necessarily band-limited, functions were awakened by a group of engineers at Aachen; applications of the theory have never been far from his thinking in this area.
- Let us look briefly at the books that Butzer has published, with the help of some of his students.
- Two years later Butzer published (with Rolf J Nessel) Fourier analysis and approximation.
- Butzer and Nessel and the publishers have been very concerned to ease the problems of the student and are to be commended.
- In 1981 Butzer edited, in collaboration with F Fehér, E B Christoffel: The Influence of His Work on Mathematics and the Physical Sciences.
- As well as editing the book, Butzer contributed an excellent article on the life and work of Christoffel.
- Similarly, in 1993 Butzer edited, in collaboration with Dietrich Lohrmann, Science in Western and Eastern Civilization in Carolingian Times.
- Finally we note that Butzer has received many honours for his outstanding contributions.

Born 15 April 1928, Mülheim an der Ruhr, Ruhr, Germany.

View full biography at MacTutor

Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive