Loewner's theorem for kernels having a finite number of negative squares

D. Alpay, J. Rovnyak

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


By a theorem of Loewner, a continuously differentiable real-valued function on a real interval whose difference quotient is a nonnegative kernel is the restriction of a holomorphic function which has nonnegative imaginary part in the upper half-plane and is holomorphic across the interval. An analogous result is obtained when the difference-quotient kernel has a finite number of negative squares.

Original languageEnglish
Pages (from-to)1109-1117
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - 1 Jan 1999


  • Loewner
  • Löwner
  • Negative squares
  • Nevanlinna
  • Pick
  • Pontryagin space
  • Reproducing kernel
  • Schur

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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