Some aspects of Wiener-Hopf factorization. (English) Zbl 0735.47010

Williams, David

Philos. Trans. R. Soc. Lond., Ser. A 335, No. 1639, 593-608 (1991).

The paper is well-written and the content can be given in the author’s own words as follows: ”It is written in response to requests from people in other fields to give some idea of what probabilists are doing. It gives some reformulations of the probabilistic Wiener-Hopf problem studied by R. R. London, H. P. McKean, L. C. G. Rogers, and the author [Séminaire de probabilités XVI, Univ. Strasbourg 1980/81, Lect. Notes Math. 920, 41-67 and 68-90 (1982, Zbl 0485.60072 and Zbl 0485.60073)]. One reformulatin as a problem of simultaneous reductions of quadratic forms is used to motivate another as a Riemann- Hilbert problem. In addition to trying to synthesize various results, it answers affirmatively a question of M. T. McGregor [J. Integral Equations 2, No. 2, 175-184 (1990; Zbl 0701.45003)] as to whether a useful convolution formula which he obtained in a special case holds generally. Section 4 on examples, methods, and their interrelations is the liveliest part of the paper.”.

Reviewer: M.M.Rao (Riverside)

MSC:

47A68	Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47B35	Toeplitz operators, Hankel operators, Wiener-Hopf operators

Keywords:

Wiener-Hopf factorization; convolution formula; probabilistic Wiener-Hopf problem; Riemann-Hilbert problem