To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on , 1 < p < ∞, 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-5,
author = {Aparajita Dasgupta and M. W. Wong},
title = {Spectral theory of SG pseudo-differential operators on $L^{p}(Rn)$
},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {185-197},
zbl = {1157.35128},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-5}
}
Aparajita Dasgupta; M. W. Wong. Spectral theory of SG pseudo-differential operators on $L^{p}(ℝⁿ)$
. Studia Mathematica, Tome 187 (2008) pp. 185-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-5/