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
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