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Positive polynomials and sums of squares.


Positive polynomials and sums of squares.

Marshall, Murray.

American Mathematical Society


187 pages



Mathematical surveys and monographs; v.146


Developed from lectures given by Marshall at the U. of Saskatchewan and elsewhere, this provides an elementary introduction and includes such subjects as the moment problem and applications to polynomial optimization. Marshall addresses Krivine's Positivstellensatz, the non-compact case, Archimedean T-modules, Schmudgen's Positivstellensatz, Putinar's question, the weak isotropy of quadratic forms, Scheiderer's local-global principle, and semidefinite programming and operation. Appendices cover such background material as the Tarksi-Seidenberg theorem and algebraic sets. Designed for students at the beginning graduate level, this concentrates on concrete objects, such as polynomials in n variables with real coefficients, and Marshall includes plenty of examples and new, simple proofs. He also provides a very useful bibliography for further study.

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Article Type:Book Review
Date:Jun 1, 2008
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