Spectral theory of SG pseudo-differential operators on $L^{p}(ℝⁿ)$

• Autorzy: Aparajita Dasgupta , M. W. Wong
• Języki publikacji: EN

Abstrakty

EN

To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on $L^{p}(ℝⁿ)$, 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.

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 47G30: Pseudodifferential operators
• 35S05: Pseudodifferential operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 2
• Strony: 185-197

Daty

wydano

2008

Twórcy

autor

Aparajita Dasgupta

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

autor

M. W. Wong

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

Identyfikatory

DOI

10.4064/sm187-2-5