Convergence of Positive Operators

Convergence of Positive Operators

Author: Ralph Leland James

Publisher:

Published: 1970

Total Pages: 164

ISBN-13:

DOWNLOAD EBOOK

The extension and convergence of positive operators is investigated by means of a monotone approximation technique. Some generalizations and extensions of Korovkin's monotone operator theorem on C[0, 1] are given. The concept of a regular set is introduced and it is shown that pointwise convergence is uniform on regular sets. Regular sets are investigated in various spaces and some characterizations are obtained. These concepts are applied to the approximate solution of a large class of integral equations.


Birkhoff Interpolation

Birkhoff Interpolation

Author: G. G. Lorentz

Publisher: Cambridge University Press

Published: 1984-12-28

Total Pages: 308

ISBN-13: 9780521302395

DOWNLOAD EBOOK

This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines.


Encyclopaedia of Mathematics

Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 595

ISBN-13: 9401512884

DOWNLOAD EBOOK

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.


Positivity and its Applications

Positivity and its Applications

Author: Eder Kikianty

Publisher: Springer Nature

Published: 2021-07-22

Total Pages: 321

ISBN-13: 3030709744

DOWNLOAD EBOOK

This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.


Summing and Nuclear Norms in Banach Space Theory

Summing and Nuclear Norms in Banach Space Theory

Author: G. J. O. Jameson

Publisher: Cambridge University Press

Published: 1987-07-30

Total Pages: 189

ISBN-13: 0521341345

DOWNLOAD EBOOK

This textbook is an introduction to the techniques of summing and nuclear norms. The author's aim is to present a clear and simple account of these ideas and to demonstrate the power of their application to a variety of Banach space questions. The style is expository and the only prerequisite is a beginner's course on Wormed linear spaces and a minimal knowledge of functional analysis. Thus, Dr Jameson is able to concentrate on important, central results and gives concrete and largely non-technical proofs, often supplying alternative proofs which both contribute something to the understanding. Final-year undergraduates and postgraduates in functional analysis will enjoy this introduction to the subject, and there are many examples and exercises throughout the text to help the reader and to demonstrate the range of application these techniques find. A list of references indicates the way for further reading.


Approximation Theory Using Positive Linear Operators

Approximation Theory Using Positive Linear Operators

Author: Radu Paltanea

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 208

ISBN-13: 1461220580

DOWNLOAD EBOOK

Offers an examination of the multivariate approximation case Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators Many general estimates, leaving room for future applications (e.g. the B-spline case) Extensions to approximation operators acting on spaces of vector functions Historical perspective in the form of previous significant results


Functional Analysis: Surveys and Recent Results III

Functional Analysis: Surveys and Recent Results III

Author: K.-D. Bierstedt

Publisher: Elsevier

Published: 2000-04-01

Total Pages: 397

ISBN-13: 0080872018

DOWNLOAD EBOOK

This volume contains 22 articles on topics of current interest in functional analysis, operator theory and related areas. Some of the papers have connections with complex function theory in one and several variables, probability theory and mathematical physics.Surveys of some areas of recent progress in functional analysis are given and related new results are presented. The topics covered in this volume supplement the discussion of modern functional analysis in the previous Proceedings volumes. Together with the previous volumes, the reader obtains a good impression of many aspects of present-day functional analysis and its applications. Parts of this volume can be used profitably in advanced seminars and courses in functional analysis.