### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**L ^{p}spectra of pseudodifferential operators generating integrated semigroups.** / Hieber, Matthias Georg.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Lpspectra of pseudodifferential operators generating integrated semigroups

AU - Hieber, Matthias Georg

PY - 1995

Y1 - 1995

N2 - Consider the Lp-realization Opp(a) of a pseudodifferential operator with symbol a ϵsm p, 0having constant coefficients. We show that for a certain class of symbols the spectrum of Opp(a) is independent of p. This implies that Opp(a) generates an TV-times integrated semigroup on W(W) for a certain N if and only if pOpp(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 Lp(Rn) if and only if p is sufficiently close to 2.

AB - Consider the Lp-realization Opp(a) of a pseudodifferential operator with symbol a ϵsm p, 0having constant coefficients. We show that for a certain class of symbols the spectrum of Opp(a) is independent of p. This implies that Opp(a) generates an TV-times integrated semigroup on W(W) for a certain N if and only if pOpp(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 Lp(Rn) if and only if p is sufficiently close to 2.

UR - http://www.scopus.com/inward/record.url?scp=84968469658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968469658&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1995-1303120-5

DO - 10.1090/S0002-9947-1995-1303120-5

M3 - Article

VL - 347

SP - 4023

EP - 4035

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 10

ER -