论文标题
加权周期性和离散伪差异操作员
Weighted periodic and discrete Pseudo-Differential Operators
论文作者
论文摘要
在本文中，我们研究了与加权符号类$ m_ {ρ，λ}^m（\ Mathbb {t} \ times \ times \ times \ mathbb {z}）$相关的伪分别计算的元素伴随，转置。我们还构建了$ M $ - elliptic pseudo-differential Operators的参数，$ \ mathbb {t} $。此外，我们证明了Gohberg的引理版本的伪划分运算符，具有加权符号类$ M_ {ρ，λ}^0（\ Mathbb {t} \ times \ times \ times \ times \ times \ mathbb {z}）$，作为应用程序，我们提供了足够的条件，以确保对相应的pseient compacte compacte compacte compacte compacte compacte compacte compacte $ l^2（\ mathbb {t}）$。最后，我们分别提供$ m $ elliptic运算符的Gårding和SharpGårding在$ \ Mathbb {z} $和$ \ Mathbb {t} $上的不平等，并在pseudo-differation $t_σu = f $ in $t_σu = f $ in $ l^psseudo-differential方案中呈现$ l^{2} $ right（pseudo-differential equientation $ t_t f $ in pseudo-differential方案）的应用程序。
In this paper, we study elements of symbolic calculus for pseudo-differential operators associated with the weighted symbol class $M_{ρ, Λ}^m(\mathbb{ T}\times \mathbb{Z})$ (associated to a suitable weight function $Λ$ on $\mathbb{Z}$) by deriving formulae for the asymptotic sums, composition, adjoint, transpose. We also construct the parametrix of $M$-elliptic pseudo-differential operators on $\mathbb{ T}$. Further, we prove a version of Gohberg's lemma for pseudo-differetial operators with weighted symbol class $M_{ρ, Λ}^0(\mathbb{ T}\times \mathbb{Z})$ and as an application, we provide a sufficient and necessary condition to ensure that the corresponding pseudo-differential operator is compact on $L^2(\mathbb{T})$. Finally, we provide Gårding's and Sharp Gårding's inequality for $M$-elliptic operators on $\mathbb{Z}$ and $\mathbb{T}$, respectively, and present an application in the context of strong solution of the pseudo-differential equation $T_σ u=f$ in $L^{2}\left(\mathbb{T}\right)$.
