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J Eng Math (2007) 59:351358 DOI 10.1007/s10665-007-9195-x

Summary: J Eng Math (2007) 59:351­358
DOI 10.1007/s10665-007-9195-x
A brief historical perspective of the Wiener­Hopf technique
Jane B. Lawrie · I. David Abrahams
Received: 16 August 2007 / Accepted: 16 August 2007 / Published online: 17 October 2007
© Springer Science+Business Media B.V. 2007
Abstract It is a little over 75 years since two of the most important mathematicians of the 20th century collabo-
rated on finding the exact solution of a particular equation with semi-infinite convolution type integral operator. The
elegance and analytical sophistication of the method, now called the Wiener­Hopf technique, impress all who use
it. Its applicability to almost all branches of engineering, mathematical physics and applied mathematics is borne
out by the many thousands of papers published on the subject since its conception. The Wiener­Hopf technique
remains an extremely important tool for modern scientists, and the areas of application continue to broaden. This
special issue of the Journal of Engineering Mathematics is dedicated to the work of Wiener and Hopf, and includes
a number of articles which demonstrate the relevance of the technique to a representative range of model problems.
Keywords Eberhard Hopf · Norbert Wiener · Wiener filter · Wiener­Hopf technique
1 Norbert Wiener and Eberhard Hopf
In retrospect, it seems an unlikely collaboration: American born Norbert Wiener (1894­1964) and Austrian born
Eberhard Hopf (1902­1983). The former was of European Jewish descent1 whilst the latter was educated in Berlin
and, despite the prevailing political climate of 1930s Germany, chose to return from a position at the Massachusetts
Institute of Technology (MIT) to take up a chair at the University of Leipzig in 1936. Individually, both men were


Source: Abrahams, I. David - Department of Mathematics, University of Manchester


Collections: Mathematics