Global wave-front sets of Banach, Frechet and modulation space types, and pseudo-differential operators

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Coriasco, Sandro¹  Johansson, Karoline²  Toft, Joachim² 

[1] Univ Turin, Dipartimento Matemat, I-10124 Turin, Italy

[2] Linnaeus Univ, Dept Comp Sci Phys & Math, Vaxjo, Sweden

关键词: Wave front;    Fourier;    Banach space;    Modulation space;    Micro-local;    Pseudo-differential;   

DOI  :  10.1016/j.jde.2013.01.014

来源: Elsevier

【 摘 要 】

We introduce global wave-front sets WFB(f), f is an element of'(R-d), with respect to suitable Banach or Frechet spaces B. An important special case is given by the modulation spaces B = M(omega,B), where omega is an appropriate weight function and B is a translation invariant Banach function space. We show that the standard properties for known notions of wave-front set extend to WFB(f). In particular, we prove that micro-locality and micro-ellipticity hold for a class of globally defined pseudo-differential operators Op(t)(alpha), acting continuously on the involved spaces. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free