Szegö limit theorems for the harmonic oscillator

A. J.E.M. Janssen, B. Steven Zelditch

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9 Scopus citations


Let (FORMULA PRESENTED) be the harmonic oscillator Hamiltonian on L2(R), and let A be a selfadjoint DO of order O in the Beals-Fefferman class with weights (FORMULA PRESENTED). Form the measure (FORMULA PRESENTED) where, (FORMULA PRESENTED) is the compression of A onto the span of the Hermite functions with eigenvalue less than or equal to ⋌. Then one has the following Szego limit theorem: (FORMULA PRESENTED) For the special case where f(x) = x, this will be proved for a considerably wider class of operators by employing the Weyl correspondence. Moreover, by using estimates on Wigner functions of Hermite functions we are able to prove the full Szego theorem for a fairly general class of multiplication operators.

Original languageEnglish (US)
Pages (from-to)563-587
Number of pages25
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - Dec 1983
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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