The complex moment problem and subnormality: A polar decomposition approach

DOI10.1006/jfan.1998.3284zbMath1048.47500OpenAlexW1981897617MaRDI QIDQ1281645

Franciszek Hugon Szafraniec, Jan Stochel

Publication date: 1998

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/350ef63b4c1d1fa4d426b13ff8cb9352d81b5ebc

zbMATH Keywords

positive definitenesspolar decompositionreal algebraic setscharacterizations of subnormalitycomplex moment problem on real algebraic curvespositive definite extendibilitytwo-dimensional real moment problem

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Subnormal operators, hyponormal operators, etc. (47B20) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Linear operator methods in interpolation, moment and extension problems (47A57) Moment problems and interpolation problems in the complex plane (30E05) Moment problems (44A60) Semialgebraic sets and related spaces (14P10)

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Cites Work

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• Unnamed Item
• Unnamed Item
• Unnamed Item
• A remark on the multidimensional moment problem
• Problème des moments sur un compact de \({\mathbb{R}}^ n\) et décomposition de polynômes a plusieurs variables
• Analytic vectors
• The two-sided complex moment problem
• The multidimensional moment problem
• Solvability criteria for certain N-dimensional moment problems
• New conditions for subnormality
• The \(K\)-moment problem for compact semi-algebraic sets
• Moment functions on real algebraic sets
• Selfadjoint extension operators commuting with an algebra
• Extensions of Hamburger's theorem
• Boundedness of the shift operator related to positive definite forms: An application to moment problems
• Positive self-adjoint extensions of operators affiliated with a von Neumann algebra.
• Injective Morphisms of Real Algebraic Varieties
• Conditionally positive definite functions on linear spaces
• A Note on the Two-Dimensional Moment Problem
• An Example of a Positive Polynomial which is not a Sum of Squares of Polynomials A Positive, but not Strongly Positive Functional
• Shorter Notes: A Formally Normal Operator having no Normal Extension
• Formally Normal Operators Having no Normal Extensions
• Theory of Reproducing Kernels
• Integral Representations of Positive Definite Functions. II

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