Equations with Involutive Operators [Paperback]

This self-contained title demonstrates an important interplay between abstract and concrete operator theory. Key ideas are developed in a step-by-step approach, beginning with required background and historical material, and culminating in the final chapters with state-of-the-art topics. Good examples, bibliography and index make this text a valuable classroom or reference resource.

Equations with Involutive Operators demonstrates an important interplay between abstract and concrete operator theory. The focus is on the investigation of a number of equations, which, while seemingly different, are all unified by the same idea: they are all realizations of some operator equations in Banach spaces. One permeating theme in these equations involves the role of the Fredholm property.The text is carefully written, self-contained, and covers a broad range of topics and results. Key ideas are developed in a step-by step approach, beginning with required background and historical material, and culminating in the final chapters with state-of-the art topics. Experts in operator theory, integral equations, and function theory as well as students in these areas will find open problems for further investigations. The book will also be useful to engineers using operator theory and integral equation techniques. Good examples, bibliography and index make this text a valuable classroom or reference resource.Introduction * Notation * I. On Fredholmness of Singular and Convolution Operators * II. On Fredholmness of Other Singular-Type Operators * III. Functional and Singular Integral Equations with Carleman Shifts in the Case of Continuous Coefficients * IV. Two Term Equations $(A+Qb)\Varphi = f$ with an Involutive Operator $Q$: An Abstract Approach and Applications * V. Equations with Several Generalized Involutive Operators: A Matrix Abstract Approach and Applications * VI. Application of the Abstract Approach to Singular Equations on the Real Line with Fractional-LinlӢ