Alice Roth

from Wikipedia, the free encyclopedia

Alice Roth (born February 6, 1905 in Bern ; † July 22, 1977 ibid) was a Swiss mathematician who dealt with approximation theory (approximation with rational functions).

Life

Roth went to the secondary school for girls in Zurich and after graduating from high school in 1924 studied mathematics, physics and astronomy at the ETH Zurich with a diploma in 1930 with George Pólya . Afterwards she was a teacher at higher girls' schools in the Zurich area and at the same time continued to work with Pólya at the ETH, where she received her doctorate in 1938 ( approximation properties and radiation limit values ​​of meromorphic and whole functions ). This made her the second woman ever to receive a doctorate in mathematics at ETH. She received the ETH silver medal for her dissertation.

From 1940 she was a mathematics and physics teacher at the Humboldtianum in Bern , a private school. Only after her retirement in 1971 did she resume mathematical research, again on approximation theory in the complex. One of her works was jointly with Paul Gauthier from the University of Montreal and with Harvard professor Joseph L. Walsh , and she wrote three others as the sole author. In 1975 she was invited to Montreal to give a lecture. In 1976 she developed cancer and died a year later.

plant

In her dissertation, she gave the example of a compact set on which not every continuous function can be uniformly approximated by rational functions. The example was later called Swiss cheese (since Roth's construction consists of creating an infinite number of holes in the set) and was also used for the construction of other counterexamples in the theory of function spaces. Her contribution was forgotten and her result was independently rediscovered in Russia in 1952 by Mergelyan .

From her 1976 work in Canadian J. Math. (Vol. 28, p. 104) is Roth's fusion lemma, which she used for her approximation theorem, which she proved in the same work, and for Bishop's localization theorem.

literature

  • Ulrich Daepp, Paul Gauthier, Pamela Gorkin & Gerald Schmieder: Alice in Switzerland: The Life and Mathematics of Alice Roth. In: The Mathematical Intelligencer . Volume 27, 2005, No. 1, pp. 41-54

Web links

Individual evidence

  1. ^ Commentarii Mathematicae Helveticae. Volume 11, 1938, pp. 477-507, online
  2. ^ Gauthier, Roth, Walsh: Possibility of uniform rational approximation in the spherical metric. In: Canadian Journal of Mathematics. Volume 28, 1976, pp. 112-114
  3. ^ Roth: Uniform and tangential approximation by meromorphic functions on closed sets. In: Canadian J. Math. Vol. 28, 1976, pp. 104-111
  4. ↑ Roth: Uniform approximation by meromorphic functions on closed sets with continuous extension into the boundary. In: Canadian J. Math. Vol. 30, 1978, pp. 1243-1255
  5. ↑ Roth: Meromorphic Approximations . In: Commentarii Math. Helv. Volume 48, 1973, pp. 151-176
  6. ↑ Represented in Dieter Gaier : Lectures on approximation in the complex. Birkhäuser, Basel / Boston / Stuttgart 1980, ISBN 3-7643-1161-4 ; engl. Edition Lectures on complex approximation. ibid. 1987, ISBN 3-7643-3147-X , p. 123 (Fusion Lemma), p. 138 (approximation theorem)
personal data
SURNAME Roth, Alice
BRIEF DESCRIPTION Swiss mathematician
DATE OF BIRTH February 6, 1905
PLACE OF BIRTH Bern
DATE OF DEATH July 22, 1977
Place of death Bern