اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAdjoints and Formal Adjoints of Matrices of Unbounded Operators
223
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we {em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be the germs of an arbitrary matrix operator, providing most of the information about the latter {as it is the troublemaker}.
قيم البحث
اقرأ أيضاً
Building on techniques developed by Cowen and Gallardo-Guti{e}rrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space $H^{2}$. We consider some specific examples, comparing our formula with several results that were previously known.
Given a Fourier-Mukai functor $Phi$ in the general setting of singular schemes, under various hypotheses we provide both left and a right adjoints to $Phi$, and also give explicit formulas for them. These formulas are simple and natural, and recover
the usual formulas when the Fourier-Mukai kernel is a perfect complex. This extends previous work of Anno and Logvinenko, and Hernandez Ruiperez, Lopez Martin and Sancho de Salas, and has applications to the twist autoequivalences of Donovan and Wemyss.
In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and clocked type theory, and spatial and cohesive type theory. In this paper we study
modal dependent type theory: dependent type theory with an operator satisfying (a dependent version of) the K-axiom of modal logic. We investigate both semantics and syntax. For the semantics, we introduce categories with families with a dependent right adjoint (CwDRA) and show that the examples above can be presented as such. Indeed, we show that any finite limit category with an adjunction of endofunctors gives rise to a CwDRA via the local universe construction. For the syntax, we introduce a dependently typed extension of Fitch-style modal lambda-calculus, show that it can be interpreted in any CwDRA, and build a term model. We extend the syntax and semantics with universes.
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, th
e bounded components can be extracted from generally-unbounded infinitesimal generators. In conclusion the concept of module over a Banach algebra is proposed as the generalization of Banach algebra. As an application to mathematical physics, the rigorous formulation of rotation group, which consists of unbounded operators being written by differential operators, is provided using the module over a Banach algebra.
We scrutinize the possibility of extending the result of cite{ccr} to the case of q-deformed oscillator for $q$ real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whethe
r a solution of the commutation relation is bounded or not. Our {it leitmotif} is {it subnormality}. The deformation parameter $q$ is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator $C$, has two remarkable properties: it separates in the commutation relation the annihilation and creation operators from the deformation as well as it $q$-commutes with those two. This is why introducing the operator $C$ seems to be far-reaching.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
