Spectral theory of SG pseudo-differential operators on $L^p(\mathbb R^n)$

Aparajita Dasgupta¹ ; M. W. Wong²

¹ Department of Mathematics and Statistics York University 4700 Keele Street Toronto, ON, Canada M3J 1P3
² Department of Mathematics and Statistics York University 4700 Keele Street Toronto, Canada M3J 1P3

Studia Mathematica, Tome 187 (2008) no. 2, pp. 185-197

Résumé

To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on $L^p(\mathbb R^n),\,1 p \infty,$ and prove that they are equal. The domain of the minimal (= maximal) operator is explicitly computed in terms of a Sobolev space. We prove that an elliptic SG pseudo-differential operator is Fredholm. The essential spectra of elliptic SG pseudo-differential operators with positive orders and bounded SG pseudo-differential operators with orders $0,0$ are computed.

Détail

DOI : 10.4064/sm187-2-5

Keywords: every elliptic pseudo differential operator positive orders associate minimal maximal operators mathbb infty prove equal domain minimal maximal operator explicitly computed terms sobolev space prove elliptic pseudo differential operator fredholm essential spectra elliptic pseudo differential operators positive orders bounded pseudo differential operators orders computed