Geodesic
Spectral theory of SG pseudo-differential operators on $L^p(\mathbb R^n)$
Aparajita Dasgupta1 ; M. W. Wong2
1Department of Mathematics and Statistics York University 4700 Keele Street Toronto, ON, Canada M3J 1P3
2Department of Mathematics and Statistics York University 4700 Keele Street Toronto, Canada M3J 1P3
Studia Mathematica, Tome 187 (2008) no. 2, pp. 185-197
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
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

Aparajita Dasgupta  1   ; M. W. Wong  2

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 
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Aparajita Dasgupta; M. W. Wong. Spectral theory of SG pseudo-differential 
operators on $L^p(\mathbb R^n)$. Studia Mathematica, Tome 187 (2008) no. 2, pp. 185-197. doi: 10.4064/sm187-2-5

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