Equations with Involutive Operators

ISBN-13: 9781461266518 / Angielski / Miękka / 2012 / 427 str.

Nikolai Karapetiants; Stefan Samko

Opis

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.

Spis treści

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-Linear Shift * Bibliography * List of Symbols * Index

O autorze

Demonstrates a fascinating interplay between abstract and concrete
operator theory. 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. Self-contained, covering a broad range of topics and
results. Initial chapters present required background material and
lead to coverage of state-of-the art topics. Good examples,
bibliography, index, and suggestions of open problems. For students
and specialists of operator theory, integral equations, and function
theory, as well as engineers using integral equation techniques.