Abstract
We consider relations between the Friedrichs operator and constructive aspects of the Dirichlet problems for the Laplace and \({\overline \partial ^{2}}\)-operator. Then we investigate the Fourier expansions in the eigenfunctions of the Friedrichs operator. A link between a generalized Friedrichs operator and minimal nodes quadratures for complex polynomials of a fixed degree is explained. We initiate a discussion of the boundary Friedrichs operator on the Hardy space of a domain. The transformation law of the Friedrichs operator under conformal mappings leads to a modified version of it, based on a symbol function; this object will turn out to be closely related to Hankel operators. We obtain some results concerning which symbols correspond to compact operators.
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Putinar, M., Shapiro, H.S. (2001). The Friedrichs operator of a planar domain. II. In: Kérchy, L., Gohberg, I., Foias, C.I., Langer, H. (eds) Recent Advances in Operator Theory and Related Topics. Operator Theory: Advances and Applications, vol 127. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8374-0_29
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DOI: https://doi.org/10.1007/978-3-0348-8374-0_29
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