Raymond Paley
Encyclopedia
Raymond Edward Alan Christopher Paley (7 January 1907 – 7 April 1933) was an English
mathematician
. Paley was born in Bournemouth, England. He was educated at Eton
. From there he entered Trinity College, Cambridge
where he showed himself the most brilliant student among a remarkable collection of fellow undergraduates. He won a Smith's Prize
in 1930 and was
elected a fellow of Trinity College.
His contributions include the Paley construction for Hadamard matrices
(closely related to the Paley graph
s in graph theory
) and his collaboration with Norbert Wiener
in the Paley–Wiener theorem
(harmonic analysis
). He collaborated with A. Zygmund
on Fourier series
(see also Paley–Zygmund inequality
) and worked with J. E. Littlewood on what became known as Littlewood–Paley theory
, an application of real-variable techniques in complex analysis
.
On 7 April 1933, Paley died in a skiing
accident when skiing alone at an altitude of 9,600 ft in Banff, Alberta
. He was killed by an avalanche at Deception Pass, Fossil Mountain
, in the Canadian Rockies
. His death was witnessed by companions lower down the mountainside. Park wardens and a member of the Royal Canadian Mounted Police
recovered the body. He is buried in the Banff town cemetery.
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. Paley was born in Bournemouth, England. He was educated at Eton
Eton College
Eton College, often referred to simply as Eton, is a British independent school for boys aged 13 to 18. It was founded in 1440 by King Henry VI as "The King's College of Our Lady of Eton besides Wyndsor"....
. From there he entered Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
where he showed himself the most brilliant student among a remarkable collection of fellow undergraduates. He won a Smith's Prize
Smith's Prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in theoretical Physics, mathematics and applied mathematics at the University of Cambridge, Cambridge, England.- History :...
in 1930 and was
elected a fellow of Trinity College.
His contributions include the Paley construction for Hadamard matrices
Hadamard matrix
In mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal...
(closely related to the Paley graph
Paley graph
In mathematics, and specifically graph theory, Paley graphs, named after Raymond Paley, are dense undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ in a quadratic residue. The Paley graphs form an infinite family of conference...
s in graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
) and his collaboration with Norbert Wiener
Norbert Wiener
Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...
in the Paley–Wiener theorem
Paley–Wiener theorem
In mathematics, a Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform. The theorem is named for Raymond Paley and Norbert Wiener . The original theorems did not use the language of distributions,...
(harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
). He collaborated with A. Zygmund
Antoni Zygmund
Antoni Zygmund was a Polish-born American mathematician.-Life:Born in Warsaw, Zygmund obtained his PhD from Warsaw University and became a professor at Stefan Batory University at Wilno...
on Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
(see also Paley–Zygmund inequality
Paley–Zygmund inequality
In mathematics, the Paley–Zygmund inequality bounds theprobability that a positive random variable is small, in terms ofits mean and variance...
) and worked with J. E. Littlewood on what became known as Littlewood–Paley theory
Littlewood–Paley theory
In harmonic analysis, Littlewood–Paley theory is a term used to describe a theoretical framework used to extend certain results about L2 functions to Lp functions for 11, then the sequence Snj converges almost everywhere...
, an application of real-variable techniques in complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
.
On 7 April 1933, Paley died in a skiing
Skiing
Skiing is a recreational activity using skis as equipment for traveling over snow. Skis are used in conjunction with boots that connect to the ski with use of a binding....
accident when skiing alone at an altitude of 9,600 ft in Banff, Alberta
Banff, Alberta
Banff is a town within Banff National Park in Alberta, Canada. It is located in Alberta's Rockies along the Trans-Canada Highway, approximately west of Calgary and east of Lake Louise....
. He was killed by an avalanche at Deception Pass, Fossil Mountain
Fossil Mountain (Alberta)
Fossil Mountain is a mountain located south of Skoki Mountain in Banff National Park, Canada. The mountain was named in 1906 by M.P. Bridgland, of the first ascent party, after the numerous fossils that can be found on its slopes....
, in the Canadian Rockies
Canadian Rockies
The Canadian Rockies comprise the Canadian segment of the North American Rocky Mountains range. They are the eastern part of the Canadian Cordillera, extending from the Interior Plains of Alberta to the Rocky Mountain Trench of British Columbia. The southern end borders Idaho and Montana of the USA...
. His death was witnessed by companions lower down the mountainside. Park wardens and a member of the Royal Canadian Mounted Police
Royal Canadian Mounted Police
The Royal Canadian Mounted Police , literally ‘Royal Gendarmerie of Canada’; colloquially known as The Mounties, and internally as ‘The Force’) is the national police force of Canada, and one of the most recognized of its kind in the world. It is unique in the world as a national, federal,...
recovered the body. He is buried in the Banff town cemetery.