In this current manuscript, some general classes of weighted analytic function spaces in a unit disc are defined and studied. Special functions significant in both analytic T(p,q,m,s;Ψ) norms and analytic Ψ-Bloch norms serve as a framework for introducing new families of analytic classes. An application in operator theory is provided by establishing important properties of the composition-type operator Cϕ such as the boundedness and compactness with the help of the defined new classes.
It is well known that for an associative ring R, if ab has g-Drazin inverse
then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula
is so-called Cline?s formula for g-Drazin inverse, which plays an elementary
role in matrix and operator theory. In this paper, we generalize Cline?s
formula to the wider case. In particular, as applications, we obtain new
common spectral properties of bounded linear operators.
The wave operator theory of quantum dynamics is reviewed and applied to the study of line profiles and to the determination of the dynamics of interacting resonances. Energy-dependent and energy-independent effective Hamiltonians are investigated. The q-reversal effect in spectroscopy is interpreted in terms of interfering Fano profiles. The dynamics of an hydrogen atom subjected to a strong static electric field is revisited.
Estimates on Some General Classes of Holomorphic Function Spaces