Abstract
Properties of the Friedrichs operator of a planar domain, originally intended for applications to planar elasticity, are related to the geometry and function theory of the domain. We show that the spectrum of the Friedrichs operator does not, in general, determine the domain, and we provide the additional necessary complete invariants. An analysis of the Friedrichs operator of generalized quadrature domains is carried out at the abstract level and on several examples. The study of Toeplitz operators on the Bergman space of the domain comes naturally into focus.
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Putinar, M., Shapiro, H.S. (2000). The Friedrichs Operator of a Planar Domain. In: Havin, V.P., Nikolski, N.K. (eds) Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, vol 113. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8378-8_25
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DOI: https://doi.org/10.1007/978-3-0348-8378-8_25
Publisher Name: Birkhäuser, Basel
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