Percy John Daniell

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Percy John Daniell

Percy John Daniell (born January 9, 1889 in Valparaíso ; † May 25, 1946 ) was a British mathematician, who is known for the introduction of the Daniell integral and the theorem of Daniell-Kolmogorov .

Life

Daniell returned with his family (his father was an export merchant from Birmingham) from Chile to England in 1895, went to school in Birmingham and from 1907 studied on a scholarship at Cambridge University (Trinity College). In 1909 he was the last senior Wrangler in the Tripos mathematics exams , i.e. the graduate with the highest number of points. Shortly thereafter, on the initiative of Godfrey Harold Hardy and others, the system was abolished (the ranking was no longer made public, but only privately communicated to the student). Then he also took part in the Natural Science Tripos, in which he was among the best in 1911. At the end of his studies he won the Rayleigh Prize in Cambridge with an essay on diffraction theory.

He then was an assistant lecturer in mathematics at Liverpool University , where William Henry Young was his colleague. From 1914 he was at the Rice Institute in Houston, Texas, which had previously sent him a year 1912/13 to the University of Göttingen for postgraduate studies with Max Born and David Hilbert , where he was supposed to study mainly theoretical physics. There was a joint publication with Ludwig Föppl on Born's theory of the rigid body in relativity theory (part of the electron theory of that time). At the Rice Institute he was Assistant Professor of Applied Mathematics, where he turned to analysis and probability theory (with a secondary interest in mathematical logic). The real analysis professor there was Griffith C. Evans . In 1920 Daniell received a full professorship.

In 1923 he returned to England and became a professor at the University of Sheffield . This was at a center of the British steel industry and he also did some applied mathematical work in the field. During World War II he advised the UK Department of Utilities, dealing with statistics, and was involved in several research projects on automatic control. Due to overwork, his health deteriorated and he suffered a collapse, as a result of which he died shortly after the war.

His generalized integration theory (Daniell or Daniell-Stone-Integral) he introduced in 1918 and expanded it in the 1920s, with publications until 1928. The works caught the attention of Henri Lebesgue at that time and were soon after their publication by Norbert Wiener in his own work on Brownian motion . Daniell introduces his integral through a series of axioms for linear functionals in function spaces and, in contrast to the Lebesgue integral (to which it is equivalent in many cases), avoids abstract measure theory. Since it avoids measure theory, it was partly popular in the middle of the 20th century, but today measure theory and Lebesgue integral are preferred in teaching.

A product of his work on time series during World War II was the method for estimating spectral densities, later known as the Daniell window .

He is also known for Daniell-Kolmogorov's theorem in the theory of stochastic processes.

He was Vice President of the London Mathematical Society . In 1922 he received a Sc. D. at Cambridge.

He had been married to Nancy Hartshorne since 1914, with whom he had two sons and two daughters.

Fonts

  • A general form of integral, Annals of Mathematics, Volume 19, 1918, pp. 279-294
  • Integrals in an infinite number of dimensions, Annals of Mathematics, Volume 20, 1919, pp. 281-288.
  • Functions of limited variation in an infinite number of dimensions, Annals of Mathematics, Volume 21, 1919, pp. 30-38
  • Further properties of the general integral Annals of Mathematics, Volume 21, 1920, pp. 203-220
  • Integral products and probability American Journal of Mathematics, Volume 43, 1921, pp. 143-162
  • The Integral and its generalization, Rice Institute Pamphlets, Volume 8, 1921, online

literature

  • Obituary by CA Stewart, Journal of the London Mathematical Society, Volume 22, 1947, pp. 75-80 (Stewart was also a professor in Sheffield)

Web links

Individual evidence

  1. ^ VI Sobolev Daniell Integral , Encyclopedia of Mathematics
  2. ↑ After him came Eric Harold Neville and Louis Mordell and fourth William Berwick and Charles Galton Darwin . Daniell's private tutor for the exams was RA Herman, who had the best reputation at the time.
  3. ↑ On the kinematics of Born's rigid body , Nachr. Ges. Wiss. Göttingen, Math-Phys. Class, 1913, pp. 519-529
  4. ↑ He had studied the Principia Mathematica of Russell and Whitehead carefully
  5. ↑ In the memoirs of one of the leading British probability theorists David Kendall , he turned to the design of blast furnaces in Sheffield , Interview with David Bingham, Statistical Science, Volume 11, 1996, pp. 159-188. However, in 1930 he published a work The theory of flame motion , Proc. Roy. Soc. A, 126, 1930, p. 393
  6. ↑ Also named after Marshall Stone with work from 1948, Notes on Integration , Proc. Nat. Acad. Sci.
  7. ↑ The related work by Daniell is Integrals in an infinite number of dimensions , Annals of Mathematics, 1919
personal data
SURNAME Daniell, Percy John
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH January 9, 1889
PLACE OF BIRTH Valparaíso
DATE OF DEATH May 25, 1946