The method of approximate spectral projection

A method is developed for proving a classical formula for the asymptotic behavior of the spectrum in various spectral problems, with a certain estimate of the remainder. Considered as applications are linear pencils both on bounded and on unbounded regions, problems in the theory of shells, and the problem of the asymptotic behavior of a discrete spectrum accumulating to the boundary of the essential spectrum for Schrödinger and Dirac operators.
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