19,755 research outputs found

    New criteria to identify spectrum

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    In this paper we give some new criteria for identifying the components of a probability measure, in its Lebesgue decomposition. This enables us to give new criteria to identify spectral types of self-adjoint operators on Hilbert spaces, especially those of interest.Comment: 10 page

    Direct integrals and spectral averaging

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    A one parameter family of selfadjoint operators gives rise to a corresponding direct integral. We show how to use the Putnam Kato theorem to obtain a new method for the proof of a spectral averaging result

    Persistence probabilities in centered, stationary, Gaussian processes in discrete time

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    Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay faster than exponentially. It is shown that if the spectral measure is not singular, then the exponent in the persistence probability cannot grow faster than quadratically. An example that appears (from numerical evidence) to achieve this lower bound is presented.Comment: 9 pages; To appear in a special volume of the Indian Journal of Pure and Applied Mathematic