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We prove an uncertainty principle for certain eigenfunction expansions on $ L^2(mathbb{R}^+,w(r)dr) $ and use it to prove analogues of theorems of Chernoff and Ingham for Laplace-Beltrami operators on compact symmetric spaces, special Hermite operator on $ mathbb{C}^n $ and Hermite operator on $ mathbb{R}^n.$
We prove an analogue of Chernoffs theorem for the sublaplacian on the Heisenberg group and use it prove a version of Inghams theorem for the Fourier transform on the same group.
We prove an analogue of Chernoffs theorem for the Laplacian $ Delta_{mathbb{H}} $ on the Heisenberg group $ mathbb{H}^n.$ As an application, we prove Ingham type theorems for the group Fourier transform on $ mathbb{H}^n $ and also for the spectral projections associated to the sublaplacian.
In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these spaces are perfect sequence
In 1975, P.R. Chernoff used iterates of the Laplacian on $mathbb{R}^n$ to prove an $L^2$ version of the Denjoy-Carleman theorem which provides a sufficient condition for a smooth function on $mathbb{R}^n$ to be quasi-analytic. In this paper, we prove
An open system is not conservative because energy can escape to the outside. An open system by itself is thus not conservative. As a result, the time-evolution operator is not hermitian in the usual sense and the eigenfunctions (factorized solutions