Abstract
In this paper, we present a construction of frames on the Heisenberg group without using the Fourier transform. Our methods are based on the Calderón-Zygmund operator theory and Coifman’s decomposition of the identity operator on the Heisenberg group. These methods are expected to be used in further studies of several complex variables.
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.
AbstractIn this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.
Construction of Frames on the Heisenberg Groups
