Math. Model. Nat. Phenom.
Volume 13, Number 4, 2018
|Number of page(s)||17|
|Published online||23 May 2018|
Characterizations of nuclear pseudo-differential operators on ℤ with some applications
Iran University of Science and Technology,
* Corresponding author: firstname.lastname@example.org
Accepted: 21 January 2018
In this paper, we give necessary and sufficient conditions on the symbols σ, such that the corresponding pseudo-differential operators Tσ from Lp1(ℤ) into Lp2(ℤ), 1 ≤ p1,p2 < ∞, be nuclear. We show that the adjoint operators of the nuclear pseudo-differential operators from Lp′2(ℤ) into Lp′1(ℤ) are nuclear and present a necessary and sufficient condition on the symbols of the nuclear pseudo-differential operators from L2(ℤ) into L2(ℤ) to be self-adjoint. As applications, We get the symbol of the product of the nuclear operators with the bounded operators, and a necessary and sufficient condition on the symbols of nuclear operators is given to be normal.
Mathematics Subject Classification: 47G30 / 47G10
Key words: Pseudo-differential operators / bounded operators / nuclear operators / adjoint / product / normal
© EDP Sciences, 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.