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Field name	Details
Dewey Class	515
Title	Orthogonal Systems and Convolution Operators ([Ebook]) / by Robert L. Ellis, Israel Gohberg
Author	Ellis, Robert L. , 1938-
Added Personal Name	Gohberg, Israel , 1928-2009
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 2003
Physical Details	XVI, 238 pages : online resource.
Series	Operator theory : advances and applications ; 140
ISBN	9783034880459
Summary Note	In this book we study orthogonal polynomials and their generalizations in spaces with weighted inner products. The impetus for our research was a deep theorem due to M.G. Krein along with subsequent results of Krein and H. Langer. Together with our colleagues, we have worked in this area for nearly fifteen years, and the results of our research are presented here in unified form. We are grateful to the Department of mathematics at the University of Maryland in College Park and to Tel-Aviv University for their support and encouragement. The support of the Silver Family Foundation is also highly appreciated. Introduction The starting point ofthis book is a study ofthe orthogonal polynomials {qn In ?: O} obtained by orthogonalizing the power functions I, Z, z2, ... on the unit circle. The orthogonality is with respect to the scalar product defined by where the weight w is a positive integrable function on the unit circle. These ortho gonal polynomials are called the Szego polynomials associated with the weight w.:
Contents note	1 Orthogonal Polynomials and Krein’s Theorem -- 2 Reformulations of Krein’s Theorem -- 3 Inner Products on Modules and Orthogonalization with Invertible Squares -- 4 Orthogonal Matrix Polynomials -- 5 Special Class of Block Toeplitz Matrices -- 6 Orthogonal Operator-Valued Polynomials: First Generalization -- 7 Convolution Equations on a Finite Interval -- 8 Continuous Analogues of Orthogonal Matrix Polynomials -- 9 Orthogonal Operator-Valued Polynomials -- 10 Reverse, Left and Right Orthogonalization -- 11 Discrete Infinite Analogue of Krein’s Theorem -- 12 Continuous Infinite Analogue of Krein’s Theorem -- References -- Index of Symbols.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-8045-9
Links to Related Works	Subject References: Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: author . Ellis, Robert L. 1938- . Gohberg, Israel 1928-2009 . Corporate Authors: SpringerLink (Online service) . Series: Operator theory : advances and applications . Classification: 515 . 515 (DDC 22) .

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Orthogonal Systems and Convolution Operators

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