اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn m-sectorial extensions of sectorial operators
80
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In our article [15] description in terms of abstract boundary conditions of all $m$-accretive extensions and their resolvents of a closed densely defined sectorial operator $S$ have been obtained. In particular, if ${mathcal{H},Gamma}$ is a boundary pair of $S$, then there is a bijective correspondence between all $m$-accretive extensions $tilde{S}$ of $S$ and all pairs $langle mathbf{Z},Xrangle$, where $mathbf{Z}$ is a $m$-accretive linear relation in $mathcal{H}$ and $X:mathrm{dom}(mathbf{Z})tooverline{mathrm{ran}(S_{F})}$ is a linear operator such that: [ |Xe|^2leqslantmathrm{Re}(mathbf{Z}(e),e)_{mathcal{H}}quadforall einmathrm{dom}(mathbf{Z}). ] As is well known the operator $S$ admits at least one $m$-sectorial extension, the Friedrichs extension. In this paper, assuming that $S$ has non-unique $m$-sectorial extension, we established additional conditions on a pair $langle mathbf{Z},Xrangle$ guaranteeing that corresponding $tilde{S}$ is $m$-sectorial extension of $S$. As an application, all $m$-sectorial extensions of a nonnegative symmetric operator in a planar model of two point interactions are described.
قيم البحث
اقرأ أيضاً
We prove an extension theorem for ultraholomorphic classes defined by so-called Braun-Meise-Taylor weight functions and transfer the proofs from the single weight sequence case from V. Thilliez [28] to the weight function setting. We are following a
different approach than the results obtained in [11], more precisely we are working with real methods by applying the ultradifferentiable Whitney-extension theorem. We are treating both the Roumieu and the Beurling case, the latter one is obtained by a reduction from the Roumieu case.
We consider densely defined sectorial operators $A_pm$ that can be written in the form $A_pm=pm iS+V$ with $mathcal{D}(A_pm)=mathcal{D}(S)=mathcal{D}(V)$, where both $S$ and $Vgeq varepsilon>0$ are assumed to be symmetric. We develop an analog to the
Birmin-Krein-Vishik-Grubb (BKVG) theory of selfadjoint extensions of a given strictly positive symmetric operator, where we will construct all maximally accretive extensions $A_D$ of $A_+$ with the property that $overline{A_+}subset A_Dsubset A_-^*$. Here, $D$ is an auxiliary operator from $ker(A_-^*)$ to $ker(A_+^*)$ that parametrizes the different extensions $A_D$. After this, we will give a criterion for when the quadratic form $psimapstombox{Re}langlepsi,A_Dpsirangle$ is closable and show that the selfadjoint operator $widehat{V}$ that corresponds to the closure is an extension of $V$. We will show how $widehat{V}$ depends on $D$, which --- using the classical BKVG-theory of selfadjoint extensions --- will allow us to define a partial order on the real parts of $A_D$ depending on $D$. Applications to second order ordinary differential operators are discussed.
We develop a set of tools for doing computations in and of (partially) wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya category with respect to so-called Weinstein sectorial coverings and (2)
that the partially wrapped Fukaya category of a Weinstein manifold with respect to a mostly Legendrian stop is generated by the cocores of the critical handles and the linking disks to the stop. We also prove (3) a `stop removal equals localization result, and (4) that the Fukaya--Seidel category of a Lefschetz fibration with Weinstein fiber is generated by the Lefschetz thimbles. These results are derived from three main ingredients, also of independent use: (5) a Kunneth formula (6) an exact triangle in the Fukaya category associated to wrapping a Lagrangian through a Legendrian stop at infinity and (7) a geometric criterion for when a pushforward functor between wrapped Fukaya categories of Liouville sectors is fully faithful.
We report on the experimental observation of corner surface solitons localized at the edges joining planar interfaces of hexagonal waveguide array with uniform nonlinear medium. The face angle between these interfaces has a strong impact on the thres
hold of soliton excitation as well as on the light energy drift and diffraction spreading.
The Kaluza and Kle
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
