Hermitian analogues of Hilbert's 17-th problem

John P. D'Angelo

Research output: Contribution to journalArticlepeer-review


We pose and discuss several Hermitian analogues of Hilbert's 17-th problem. We survey what is known, offer many explicit examples and some proofs, and give applications to CR geometry. We prove one new algebraic theorem: a non-negative Hermitian symmetric polynomial divides a non-zero squared norm if and only if it is a quotient of squared norms. We also discuss a new example of Putinar-Scheiderer.

Original languageEnglish (US)
Pages (from-to)4607-4637
Number of pages31
JournalAdvances in Mathematics
Issue number5
StatePublished - Mar 20 2011


  • 17-th problem
  • CR complexity theory
  • Hermitian forms
  • Proper holomorphic mappings
  • Signature pairs
  • Squared norms

ASJC Scopus subject areas

  • Mathematics(all)


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