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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}.
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
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
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
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