Extremal solutions of the two-dimensional $L$-problem of moments, II

Details Extremal solutions of the two-dimensional $L$-problem of moments, II Extremal solutions of the two-dimensional $L$-problem of moments, II

1995-12-18

arxiv.org/abs/math/9512222v1

Mathematics

Classical Analysis and ODEs

Scientific paper

All extremal solutions of the truncated $L$-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality. An exponential kernel, arising as the determinantal function of a naturally associated hyponormal operator with rank-one self-commutator, provides a natural defining function for these semi-algebraic sets. We find an intrinsic characterization of this kernel and we describe a series of analytic continuation properties of it which are closely related to the behaviour of the Schwarz reflection function in portions of the boundary of the extremal supporting set.

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