University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On the Wiener-Hopf technique and its applications in science and engineering: Lecture 1

On the Wiener-Hopf technique and its applications in science and engineering: Lecture 1

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WHT - Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications

It is a little nearly 90 years since two of the most important mathematicians of the 20th century collaborated 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 Wiener-Hopf 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. 
This series of three lectures will be informal in nature and directed at researchers who are either at an early stage of their career or else unfamiliar with particular aspects of the subject. Their aim is to demonstrate the beauty of the topic and its wide range of applications, and will be delivered in a traditional applied mathematical style. The lectures will not try to offer a comprehensive overview of the literature but will instead focus on specific topics that have been of interest over the years to the speaker.   

The first lecture shall offer a subjective review of the subject, introducing the notation to be employed in later lectures, and indicating a sample of the enormous range of applications that have been found for the technique. The second lecture will focus on exact and approximate solution methods for scalar and vector Wiener-Hopf equations, and indicate the similarities and differences of the various approaches used. The final lecture shall continue discussion of approximate approaches, combining these with one or more specific applications of current interest to the speaker.



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