Stable Approximate Evaluation of Unbounded Operators

This book teams up the spectral theory of bounded linear operators with von Neumann’s theory of unbounded operators to provide a framework for the study of stable methods for the evaluation of unbounded operators. The text presents numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. It also offers an extensive exposition of background material from the theory of operators on Hilbert space.

Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.