Ellipticity and Fredholmness of Symmetrically Global Pseudo-Differential Operators on Rn
主 题: Ellipticity and Fredholmness of Symmetrically Global Pseudo-Differential Operators on Rn
报告人: Professor Wong Man Wah (York University, Canada)
时 间: 2015-11-13 15:00-16:00
地 点: 理科一号楼 1365
The global pseudo-differential operators on $\Rn$ first studied by Kohn, Nirenberg and H\"ormander, among others, have the properety that Fredholmness in $L^p(\Rn)$ for some $p\in (1,\infty),$ implies ellipticity, but the converse is not true. Of fundamental importance in the the study of pseudo-differential operators are the elliptic operators and the Fredholm operators. A good class of pseudo-differential operators is one in which ellipticity and Fredholmness are equivalent. On one hand, ellipticity is a condition involving lower order terms to ensure global regularity. On the other hand, Fredholmness means normal solvability and the function spaces in which normal solvability occurs becomes crucial. A class of pseudo-differential operators, dubbed by me {\it symmetrically global} (SG) pseudo-differential operators on $\Rn$, is shown to have the property that ellipticity and Fredholmess in $L^p(\Rn),\, 1
