### Abstract

Consider the L^{p}-realization Op_{p}(a) of a pseudodifferential operator with symbol a ϵs^{m} _{p, 0}having constant coefficients. We show that for a certain class of symbols the spectrum of Op_{p}(a) is independent of p. This implies that Op_{p}(a) generates an TV-times integrated semigroup on W(W) for a certain N if and only if pOp_{p}(a)≠ ∅ and the numerical range of a is contained in a left half-plane. Our method allows us also to construct examples of operators generating integrated semigroups on L^{p}(R^{n}) if and only if p is sufficiently close to 2.

Original language | English |
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Pages (from-to) | 4023-4035 |

Number of pages | 13 |

Journal | Transactions of the American Mathematical Society |

Volume | 347 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1995 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Hieber, M. G. (1995). L

^{p}spectra of pseudodifferential operators generating integrated semigroups.*Transactions of the American Mathematical Society*,*347*(10), 4023-4035. https://doi.org/10.1090/S0002-9947-1995-1303120-5