## Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains, Issue 1152 |

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### Contents

Introduction | 1 |

Derivation of the Series | 16 |

The Szego and Heat Expansion | 36 |

Copyright | |

7 other sections not shown

### Other editions - View all

Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains Harold Widom Limited preview - 2006 |

Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains Harold Widom No preview available - 2014 |

### Common terms and phrases

amplitude function analogue of Lemma apply Lemma assertion assume asymptotic expansion belongs boundary terms bounded operator Chapter coefficients compute constant corresponding cotangent bundle deduce define denotes derivatives diffeomorphism differentiations eigenvalues equal error incurred essential range estimates expression fact formal expansion formal series formula Fourier transform given gives heat expansion Hilbert space Hilbert transform holds homogeneous Hp(R identity incurs an error integrand interior terms invertible kernel Lemma 62 linear combination matrix multi-indices multiplication operators multiplied negative order neighborhood of sp(a notation null space obtained operator symbol operator-valued symbols P-process PaAPa polynomial proof of Lemma Proposition pseudodifferential operator Recall replaced representation result satisfying scalar Schwartz function second fundamental form self-adjoint Sobolev spaces substitution sum of terms symbol class symbol of negative symbol of order symbol of weight Szego expansion terms of weight theorem trace class trace class operator trace norm uniformly vanishes Wiener-Hopf write zero