Spectral theory of a hybrid class of pseudo-differential operators

被引：2

作者：

Alimohammady, M. ^{[1
]}

Kalleji, M. K. ^{[1
]}

机构：

[1] Univ Mazandaran, Dept Math, Fac Math Sci, Babol Sar 474161468, Iran

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2014年 / 59卷 / 12期

关键词：

SG-pseudo-differential operators; M-hypoellipticity; minimal and maximal operators; Fredholm operators; essential spectra; Primary: 35S05; 47G30; Secondary: 47A53; WAVE-FRONT SET; BOUNDARY;

D O I：

10.1080/17476933.2013.866108

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we introduce the hybrid class of the so-called SG-M-hypoelliptic symbols, and consider the corresponding pseudo-differential operators. With any SG-M-elliptic pseudo-differential operator with positive order, we associate the minimal and maximal operators on L-p(R-n), 1 < p < infinity. Further on, we prove that the minimal and maximal operators are equal and we compute their domains in terms of a family of suitable Sobolev spaces. In the last section, we show that an SG-M-elliptic pseudo-differential operator is Fredholm. Moreover, we discuss the essential spectra of SG-M-elliptic pseudo-differential operators with suitable orders.

引用

页码：1573 / 1588

页数：16

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