Linear Operators and Ill-Posed Problems [Hardcover]

In this easily-accessible textbook, the authors integrate the ill-posed problem theory and its underlying mathematical apparatus. This comprehensive work includes descriptions of recent results and a presentation of actual applications of the ill-posed problem theory. The first part of the book describes the differentiation of normed space mappings, the integration of the functions of abstract variables, and the theory of linear operators. The second section deals with the mathematical physics connected to integral equations of the first type, and with the bases of operator equation theory.Linear Operators: Differentiation. Integration. Linear Operators. Ill-Posed Problems: Classical Problems. Ill-posed Problems. Operator and Integral Equations. Evolution Equations. Problems of Integral Geometry. Supplement: Inversion Formulas in Inverse Problems A.L. Bukhgeim.: Introduction. Tomography and the Theory of Analytic Functions. Reconstruction of Phonon Spectra from the Heat Capacity Data. Index.