## Abstract

Let (FORMULA PRESENTED) be the harmonic oscillator Hamiltonian on L^{2}(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 language | English |
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Pages (from-to) | 563-587 |

Number of pages | 25 |

Journal | Transactions of the American Mathematical Society |

Volume | 280 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 1983 |

Externally published | Yes |