1st Edition

Hypersingular Integrals and Their Applications



ISBN 9780415272681
Published October 24, 2001 by CRC Press
378 Pages

 
SAVE ~ $49.00
was $245.00
USD $196.00

Prices & shipping based on shipping country


Preview

Book Description

Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.

Table of Contents

Part I: Hypersingular Integrals and Their Applications. Some Basics from the Theory of Special Functions and Operator Theory. The Reisz Potential Operator and the Lizorkin Type Invarient Spaces. Hypersingular Integrals with Constant Characteristics Potentials and Hypersingular Integrals with Non-Homogenous Characteristics. Hypersingular Integrals on the Unit Sphere. Part II: Applications of Hypersingular Integrals. Hypersingular Integrals in the Theory of Functional Spaces. Solution of Multidimensional Integral Equations of the First Kind with a Potential Type Kernel. Hypersingular Operators as Positive Fractional Powers of Some Operators of Mathematical Physics. Regularization of Integral Equations of the First Kind with a Potential Type Kernel Applications to Function Spaces on a Sphere. Some Modifications of Hypersingular Integrals and Their Applications.

...
View More