Real separated algebraic curves, quadrature domains, Ahlfors type functions and operator theory
Copyright policy )Real separated algebraic curves, quadrature domains, Ahlfors type functions and operator theory
The aim of this paper is to inter-relate several algebraic and analytic objects, such as real-type algebraic curves, quadrature domains, functions on them and rational matrix functions with special properties, and some objects from Operator Theory, such as vector Toeplitz operators and subnormal operators. Our tools come from operator theory, but some of our results have purely algebraic formulation. We make use of Xia's theory of subnormal operators and of the previous results by the author in this direction. We also correct (in Section 5) some inaccuracies in two papers by the author in Revista Matematica Iberoamericana (1998).
43 pages, 2 figures; zip archive
General theory of conformal mappings, subnormal operator, FOS: Physical sciences, Klein surface, Schottky double, Miscellaneous applications of operator theory, Mathematics - Spectral Theory, quadrature domain, Mathematics - Algebraic Geometry, Linear operators on function spaces (general), Primary 47B20, Secondary 30F50, 14H45, FOS: Mathematics, Complex Variables (math.CV), Analytic vector, Spectral Theory (math.SP), Algebraic Geometry (math.AG), Mathematical Physics, bepress|Physical Sciences and Mathematics|Mathematics, Functional analysis techniques applied to functions of several complex variables, Mathematics - Complex Variables, Mathematical Physics (math-ph), Subnormal operator, Real algebraic sets, Toeplitz operator, Quadrature domain, Toeplitz operators, Hankel operators, Wiener-Hopf operators, bepress|Physical Sciences and Mathematics|Mathematics|Algebraic Geometry, Subnormal operators, hyponormal operators, etc., Analysis
General theory of conformal mappings, subnormal operator, FOS: Physical sciences, Klein surface, Schottky double, Miscellaneous applications of operator theory, Mathematics - Spectral Theory, quadrature domain, Mathematics - Algebraic Geometry, Linear operators on function spaces (general), Primary 47B20, Secondary 30F50, 14H45, FOS: Mathematics, Complex Variables (math.CV), Analytic vector, Spectral Theory (math.SP), Algebraic Geometry (math.AG), Mathematical Physics, bepress|Physical Sciences and Mathematics|Mathematics, Functional analysis techniques applied to functions of several complex variables, Mathematics - Complex Variables, Mathematical Physics (math-ph), Subnormal operator, Real algebraic sets, Toeplitz operator, Quadrature domain, Toeplitz operators, Hankel operators, Wiener-Hopf operators, bepress|Physical Sciences and Mathematics|Mathematics|Algebraic Geometry, Subnormal operators, hyponormal operators, etc., Analysis
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