A study on the adjoint of pseudo-differential operators on compact lie groups. Issue 10 (3rd October 2018)

• Record Type: Journal Article
• Authors: Ghaemi, M. B.; Nabizadeh, E.; Jamalpour, M.; Kalleji, M. K.
• Is Part Of: Complex variables and elliptic equations. Volume 63:Issue 10(2018)
• Page Start: 1408
• Page End: 1420
• Publication Date: 2018-10-03
• Subjects: Pseudo-differential operator -- compact Lie group -- self-adjointness -- normal operator -- unitary operator; 47G30 -- 35S05 -- 22E30 -- 43A77 -- 22C05; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2017.1376188
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract: In this paper we find a formula for the adjoint of bounded pseudo-differential operators on compact Lie groups, which yields a necessary and sufficient condition for self-adjointness of these operators. By a similar method we find necessary and sufficient conditions for bounded pseudo-differential operators on compact Lie groups to be normal or unitary and we give some examples of our results onS 1 . Then we show that similar results are true for some bounded pseudo-differential operators onZ .