M -elliptic pseudo-differential operators on Lp(ℝn)

✍ Scribed by M. W. Wong

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 140 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310363

✦ Synopsis

Abstract

We construct the minimal and maximal extensions in L ^p^ (ℝ^n^ ), 1 < p < ∞, for M ‐elliptic pseudo‐differential operators initiated by Garello and Morando. We prove that they are equal and determine the domains of the minimal, and hence maximal, extensions of M ‐elliptic pseudo‐differential operators. For M ‐elliptic pseudodifferential operators with constant coefficients, the spectra and essential spectra are computed. An application to quantization is given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)