Mathematical Research Letters

Volume 17 (2010)

Number 6

Sums of hermitian squares on pseudoconvex boundaries

Pages: 1047 – 1053



Mihai Putinar (University of California at Santa Barbara)

Claus Scheiderer (Universität Konstanz, D-78457 Konstanz, Germany)


We give an abstract characterization of all real algebraic subvarieties of complex affine space on which every positive polynomial is a sum of hermitian squares, and we find obstructions to this phenomenon. As a consequence we construct a strictly pseudoconvex domain with smooth algebraic boundary on which there exists a degree two positive polynomial which is not a sum of hermitian squares, answering thus in the negative a question of John D'Angelo.

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