Classes of Compact Operators and Eigenvalue Distributions for Elliptic Operators

Abstract

the characteristic values of compact operators which may be of independent interest. These are established in Sections 1 and 2 and are applied in Section 3 to general operators with compact resolvent. Applications to spaces of distributions and to elliptic operators are given in Sections 4 and 5. The asymptotic formula for the eigenvalues of classical second order operators is due to Weyl [12]. His results were rederived by Carleman, using a powerful method which has been applied to more general elliptic problems by Pleijel, Browder, Garding, Agmon, and others; see [1], [7], and the references there. However, this method demands more regularity of the coefficients of the operator than seems necessary for validity of the formula. In an earlier paper [5] the author extended the formula to the Dirichlet problem under minimal assumptions on the coefficients, by approximation argument in the spirit of that of Weyl. The present paper establishes the result for coercive (differential) boundary value problems and for certain non-local