A FACTORIZATION PROBLEM IN NORMED RINGS, FUNCTIONS OF ISOMETRIC AND SYMMETRIC OPERATORS AND SINGULAR INTEGRAL EQUATIONS

Abstract

CONTENTSIntroductionChapter I. Factorization of matrix-functions in normed rings § 1. General theorems on factorization of matrix-functions in normed rings § 2. Proof of the fundamental theorem on factorization of matrix-functions § 3. Stability theorems for systems of indices § 4. GeneralizationsChapter II. Functions of isometric and symmetric operators § 5. Continuous functions of one-sidedly invertible elements § 6. Functions of isometric operators § 7. Applications to operators generated by Toeplitz matrices § 8. Functions of a maximal symmetric operator. Continuous analogues of operators generated by Toeplitz matricesChapter III. Theorems on one-sided invertibility of elements and their applications § 9. A theorem on one-sided invertibility for special classes of elements of normed rings § 10. Applications to functions of isometric operators § 11. Generalizations of theorems on one-sided invertibility of elements. Applications to singular integral equationsReferences