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- W2015282500 abstract "In this paper we consider asymptotic behaviour of spectral function of an elliptic differential (pseudodifferential) equation or system of equations. For case of differential operators this problem has been widely studied, and various methods have been developed for its solution (see [1] and [2] for a survey of these methods). We consider in this paper just one of these methods. It is based on a study of structure of fundamental solution of Cauchy problem for a hyperbolic differential (pseudodifferential) equation. The method we use is called the method of geometrical optics. For a system of first order differential equations it was originally developed in detail by Lax [8], and for pseudodifferential equations by Hormander [2] and independently by Eskin [17], [18] and Maslov [19]. In [2] Hormander also investigates asymptotic behaviour of spectral function for an elliptic pseudodifferential first order operator. Using some important results of Seeley [5] one can then derive asymptotic behaviour of spectral function of an elliptic differential operator of arbitrary order. Similar methods have previously been applied by author in [3], [4] for second order elliptic differential operators. In this article we give a partial account of results of [8] and [2]. We also present some new results due to author, concerning both structure of fundamental solution of Cauchy problem and asymptotic behaviour of spectral function." @default.
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- W2015282500 date "1971-12-31" @default.
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- W2015282500 title "ASYMPTOTIC BEHAVIOUR OF THE SPECTRAL FUNCTION OF AN ELLIPTIC EQUATION" @default.
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