Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T06:46:10.127Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of Compact SG Pseudo-differential Operatorson L2(ℝn)

Published online by Cambridge University Press:  17 July 2014

S. Molahajloo
Get access

Abstract

We give a necessary and sufficient condition for pseudo-differential operators with SGsymbols to be compact from L2(ℝn)into L2(ℝn).

Keywords

SG pseudo–differential operatorscompact operatorsCalkin algebraFredholmnessessential spectra
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 5: Spectral problems , 2014 , pp. 239 - 243
Copyright
© EDP Sciences, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Atkinson, F. V.. The normal solvability of linear equations in normed spaces (Russian). Mat. Sbornik N. S., 28 (1951), no. 70, 3–14. Google Scholar
P. Boggiatto, E. Buzano, L. Rodino. Global Hypoellipticity and Spectral Theory. Akademie-Verlag, 1996.
Cappiello, M., Rodino, L.. SG-pseudo-differential operators and Gelfand–Shilov spaces. Rocky Mountain J. Math., 36 (2006), 1117-1148. CrossRefGoogle Scholar
S. Coriasco, L. RodiCauchy problem for SG-hyperbolic equations with constant multipliers. no. Ricerche Mat. Suppl., XLVIII (1999), 25-43.
Dasgupta, A., Wong, M. W.. Spectral theory of SG pseudo-differential operators on Lp(ℝn). Studia Math., 187 (2008), 186–197. CrossRefGoogle Scholar
Y. V. Egorov, B.-W. Schulze. Pseudo-Differential Operators, Singularities, Applications. Birkhäuser, 1997.
Grushin, V. V.. Pseudodifferential operators on ℝn with bounded symbols. Funct. Anal. Appl., 4 (1970), 202–212. CrossRefGoogle Scholar
L. Hörmander. The Analysis of Linear Partial Differential Operators III: Pseudo-Differential Operators. Reprint of the 1994 Edition, Classics in Mathematics, Springer-Verlag, 2007.
S. Molahajloo. A characterization of compact pseudo-differential operators on S1. in Pseudo-Differential Operators: Analysis, Applications and Computations, Operator Theory: Advances and Applications, Birkhäuser, 213 (2011), 25–29.
Molahajloo, S., Wong, M. W.. Ellipticity, Fredholmness and spectral invariance of pseudo-differential operators on S1. J. Pseudo-Differ. Oper. Appl, 1 (2010), 183–205. CrossRefGoogle Scholar
Nicola, F.. K-theory of SG-pseudo-differential algebras. Proc. Amer. Math. Soc., 131 (2003), 2841-2848. CrossRefGoogle Scholar
Schechter, M.. On the essential spectrum of an arbitrary operator I. J. Math. Anal. Appl., 13 (1966), 205–215. CrossRefGoogle Scholar
M. Schechter. Spectra of Partial Differential Operators. Second Edition, North-Holland, 1986.
Wolf, F.. On essential spectrum of partial differential boundary problems. Comm. Pure Appl. Math., 12 (1959), 211-228. CrossRefGoogle Scholar
M. W. Wong. An Introduction to Pseudo-Differential Operators. Second Edition, World Scientific, 1999.