This is a survey of the classical Cesàro operator aimed at graduate students as well as more experienced researchers. The eleven chapters of the book cover topics from Cesàro's early work on summability of series and continues with the seminal paper of Brown, Halmos, and Shields on the Cesàro operator.

Along the way, various normality classes of the Cesàro operator are covered, as well as invariant subspaces and semigroups. Recent and ongoing work concerning generalizations of the Cesàro operator is also included.

The book also features detailed endnotes for each chapter with historical references and suggestions for further reading.

Autorentext

William T. Ross: Prof Ross is the Richardson Professor of Mathematics at the University of Richmond and is the author of over 80 research papers in mathematics and 8 research monographs. He is also an editor for Concrete Operators, Canadian Mathematical Bulletin, and the Canadian Journal of Mathematics.

Professor Javad Mashreghi is the Canada Research Chair in Function Spaces and their Applications at Laval University. He has served two terms as President of the Canadian Mathematical Society and is a Fellow of the American Mathematical Society, the Canadian Mathematical Society, and the Fields Institute. He has authored more than 150 research papers in mathematics and over 15 textbooks and monographs, many of which have become influential references in analysis and operator theory.

Inhalt

Chapter.1.Ernesto Cesaro.- Chapter 2.Cesaro Summability,- Chapter 3.The Cesaro Matrix.- Chapter 4.The Cesaro Operator on the Space of Analytic Functions.- Chaper.5.The Cesaro Operator on the Hardy Space.- Chapter 6.Normality Classes and the Cesaro Operator.- Chapter 7 Fredholm Theory for the Cesaro Operator.- Chapter 8.The Cesaro Operator and Semigroups.- Chapter 9.Invariant Subspaces of the Cesaro Operator.- Chapter 10.The Continuous Cesaro Operators.- Chapter.11.Generalized Ces`aro Operators.-References.-Author Index.-Subject Index.