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Classification of Toeplitz operators on Hardy spaces of bounded domains in the plane. (English) Zbl 1443.47031

Summary: We construct an orthonormal basis for the class of square integrable functions on bounded domains in the plane in terms of the classical kernel functions in potential theory. Then we generalize the results of A. Brown and P. R. Halmos [J. Reine Angew. Math. 213, 89–102 (1963; Zbl 0116.32501)] about algebraic properties of Toeplitz operators and Laurent operators on the unit disc to general bounded domains. This is a complete classification of Laurent operators and Toeplitz operators for bounded domains.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
30H10 Hardy spaces
30C40 Kernel functions in one complex variable and applications
31A10 Integral representations, integral operators, integral equations methods in two dimensions

Citations:

Zbl 0116.32501
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Full Text: DOI

References:

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[7] Y.-B. Chung, “Toeplitz operators on bounded domains in the plane,” (in submission). · Zbl 1443.47031
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