Mit 6.972 Algebraic Techniques and Semidefinite Optimization
نویسنده
چکیده
In this lecture we introduce Schmüdgen’s theorem about the Kmoment problem (or equivalently, on the representation of positive polynomials) and describe the basic elements in his proof. This approach combines both algebraic tools (using the Positivstellensatz to prove the boundedness of certain operators) and functional analysis (spectral measures of commuting families of operators and the HahnBanach theorem). We will also describe some alternative versions due to Putinar, as well as a related purely functionalanalytic result due to Megretski. For a comprehensive treatment and additional references, we mention [BCR98, Mar00, PD01] among others.
منابع مشابه
Mit 6.972 Algebraic Techniques and Semidefinite Optimization Lecture 8
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