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Extremal Solutions of the Two-DimensionalL-Problem of Moments

✍ Scribed by Mihai Putinar

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
817 KB
Volume
136
Category
Article
ISSN
0022-1236

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✦ Synopsis

By using the theory of the principal function of a hyponormal operator with rank-one self-commutator, one classifies some extremal points of the solutions of the truncated L-problem of moments in two real variables. These extremal elements, called degenerated solutions of the L-problem, are proved to be in a natural bijective correspondence with the bounded quadrature domains in the complex plane. The main result of the paper characterizes these degenerated solutions from three distinct perspectives: complex analysis, moment problems, and operator theory. The interplay between the three points of view, each with specific techniques, constitutes the main body of the paper.

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