The Growth of the Resolvent Operator and Applications to Completeness
The behaviour of the resolvent in a neighbourhood of the spectrum is one of the important characteristics of an operator. The first section presents a basic theorem in which a sharp evaluation is given of the norm of an inverse operator in terms of the determinant and the singular values. The theorem is used in the second section to evaluate the growth of the resolvent of a Volterra operator. The applications concern two completeness theorems, which are presented in the last two sections.
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