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...
In this book we study orthogonal polynomials and their generalizations in spaces with weighted inner products. The impetus for our research was a deep...
This is the second volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The second part of the present volume collects nonself-adjoint problems on small motions and normal oscillations of a viscous fluid filling a bounded region.
This is the second volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical m...
The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition. The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems,...
The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochas...
Many problems of the engineering sciences, physics, and mathematics lead to con- volution equations and their various modifications. Convolution equations on a half-line can be studied by having recourse to the methods and results of the theory of Toeplitz and Wiener-Hopf operators. Convolutions by integrable kernels have continuous symbols and the Cauchy singular integral operator is the most prominent example of a convolution operator with a piecewise continuous symbol. The Fredholm theory of Toeplitz and Wiener-Hopf operators with continuous and piecewise continuous (matrix) symbols is...
Many problems of the engineering sciences, physics, and mathematics lead to con- volution equations and their various modifications. Convolution equat...
The following tract is divided into three parts: Hilbert spaces and their (bounded and unbounded) self-adjoint operators, linear Hamiltonian systemsand their scalar counterparts and their application to orthogonal polynomials. In a sense, this is an updating of E. C. Titchmarsh's classic Eigenfunction Expansions. My interest in these areas began in 1960-61, when, as a graduate student, I was introduced by my advisors E. J. McShane and Marvin Rosenblum to the ideas of Hilbert space. The next year I was given a problem by Marvin Rosenblum that involved a differential operator with an "integral"...
The following tract is divided into three parts: Hilbert spaces and their (bounded and unbounded) self-adjoint operators, linear Hamiltonian systemsan...
In September 1998, during the 'International Workshop on Analysis and Vibrat- ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occasion of his 70th birthday with a volume in the series 'Operator Theory: Advances and Applications'. Friends and colleagues responded enthusiastically to this proposal and within a short time we put together the volume which is now presented to the reader. Regarding accep- tance of papers we followed the usual rules of the journal 'Integral Equations and Operator Theory'. The papers are...
In September 1998, during the 'International Workshop on Analysis and Vibrat- ing Systems' held in Canmore, Alberta, Canada, it was decided by a group...
This volume is dedicated to Bernd Silbermann on the oc- casion of his sixtieth birthday. It consists of selected papers devoted to the inexhaustible and ever-young fields of Toeplitz matrices and singular integral equations, and thus to areas Bernd Silbermann has been enriching by fundamental con- tributions for the last three decades. Most authors of this volume participated in the conference organized and sponsored by the Department of Mathematics (under the deans Dieter Happel and Jiirgen vom Scheidt) of the Chemnitz University of Technology in honor of Bernd Silbermann in Pobershau, April...
This volume is dedicated to Bernd Silbermann on the oc- casion of his sixtieth birthday. It consists of selected papers devoted to the inexhaustible a...
We offer the reader of this book some specimens of "infinity" that we seized from the "mathematical jungle" and trapped within the solid cage of analysis The creation of the theory of singular integral equations in the mid 20th century is associated with the names of N.1. Muskhelishvili, F.D. Gakhov, N.P. Vekua and their numerous students and followers and is marked by the fact that it relied principally on methods of complex analysis. In the early 1960s, the development of this theory received a powerful impulse from the ideas and methods of functional analysis that were then brought into...
We offer the reader of this book some specimens of "infinity" that we seized from the "mathematical jungle" and trapped within the solid cage of analy...
This volume is based on the proceedings of the Toeplitz Lectures 1999 and of the Workshop in Operator Theory held in March 1999 at Tel-Aviv University and at the Weizmann Institute of Science. The workshop was held on the occasion of the 60th birthday of Harry Dym, and the Toeplitz lecturers were Harry Dym and Jim Rovnyak. The papers in the volume reflect Harry's influence on the field of operator theory and its applications through his insights, his writings, and his personality. The volume begins with an autobiographical sketch, followed by the list ofpublications ofHarry Dym and the paper...
This volume is based on the proceedings of the Toeplitz Lectures 1999 and of the Workshop in Operator Theory held in March 1999 at Tel-Aviv University...
This book is based on lectures given at the Global Analysis Research Center (GARC) of Seoul National University in 1999and at Peking University in 1999and 2000. Preliminary versions of the book have been used for various topics courses in analysis for graduate students at York University. We study in this book wavelet transforms and localization operators in the context of infinite-dimensional and square-integrable representations of locally compact and Hausdorffgroups. The wavelet transforms studied in this book, which include the ones that come from the Weyl-Heisenberg group and the...
This book is based on lectures given at the Global Analysis Research Center (GARC) of Seoul National University in 1999and at Peking University in 199...
