How to solve an equation with a Toeplitz operator?
An equation with a Hardy space Toeplitz operator can be solved by Wiener–Hopf factorization. However, Wiener–Hopf factorization does not work for Bergman space Toeplitz operators. The only way we see to tackle equations with a Toeplitz operator on the Bergman space is to have recourse to approximation methods. The paper is intended as a review of and an illustrated tour through several such methods and thus through some beautiful topics in the intersection of operator theory, complex analysis, differential geometry, and numerical mathematics.
KeywordsToeplitz operator Hardy space Wiener–Hopf factorization Bergman space Bergman kernel complex approximation
MSC 2010Primary 47B35 Secondary 30E10 30H20 65R20
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