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.
Life
Daniell returned with his family (his father was an export merchant of Birmingham) in 1895 from Chile to England, went to school in Birmingham and studied from 1907 with a scholarship at the University of Cambridge ( Trinity College). In 1909, he was there in the Tripos examinations of Mathematics of the last Senior Wrangler, so the graduate with the highest score. Shortly afterwards, was abolished at the initiative of Godfrey Harold Hardy and other system ( the ranking was not made more public but only privately communicated to the students). He then also took to the Natural Science Tripos in part, in which he came also among the top 1911. At the conclusion of his studies he won the Rayleigh Price in Cambridge with an essay on the theory of diffraction.
After that, he was at Liverpool University as an Assistant Lecturer in Mathematics, where William Henry Young was his colleague. From 1914 he was in Houston, Texas, for a year before the 1912/13, to the University of Göttingen sent him to postgraduate study with Max Born and David Hilbert, where he should study mainly theoretical physics at Rice Institute. There, a joint publication with Ludwig Foppl on Born's theory of the rigid body in relativity theory arose (part of the then- electron theory ). At the Rice Institute, he was an Assistant Professor of Applied Mathematics and turned there of analysis and probability theory ( with a side interest in mathematical logic). The actual Analysis Professor Griffith C. Evans was there. 1920 Daniell received a full professorship.
In 1923 he returned to England and became a professor at the University of Sheffield. This was in a center of the British steel industry and he made some applied mathematical work on this Gebiet.Im World War II he advised the British Ministry of Supply, where he dealt with statistics, and was involved in several research projects for automatic control. Due to overwork his health suffered and he suffered a breakdown, as a result he died shortly after the war.
His generalized theory of integration ( Daniell and Daniell -Stone - integral), he led in 1918 and expanded it in the 1920s from, with publications until 1928. The work then found the attention of Henri Lebesgue and were soon after publication of Norbert Wiener in his used own work on Brownian motion. Daniells leads his integral over a set of axioms for linear functionals in functional spaces and avoids in contrast to the Lebesgue integral (to which it is in many cases equivalent) the abstract measure theory. Since the measure theory it was partially avoids the mid-20th century popular today but is preferably in the teaching measure theory and Lebesgue integral.
A product of his labor during World War II over the time series was later called Daniell window method for estimation of spectral densities.
He is also known for the extended set of Daniell and Kolmogorov in the theory of stochastic processes.
He was Vice- President of the London Mathematical Society. In 1922, he received a Sc. D. Cambridge.
He was married in 1914 to Nancy Hartshorne, with whom he had two sons and two daughters.
Writings
- A general form of integral, Annals of Mathematics, Volume 19, 1918, pp. 279-294
- To the integral in infinite number of dimensions, Annals of Mathematics, Volume 20, 1919, pp. 281-288.
- Functions of limited variation in a infinite number of dimensions, Annals of Mathematics, Volume 21, 1919, pp. 30-38
- Integral products and probability American Journal of Mathematics, Volume 43, 1921, pp. 143-162
- The integral and its generalization, Rice Institute Pamphlet, Volume 8, 1921, Online