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Author: Radu Paltanea Publisher: Springer Science & Business Media ISBN: 1461220580 Category : Mathematics Languages : en Pages : 208
Book Description
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
Author: Radu Paltanea Publisher: Springer Science & Business Media ISBN: 1461220580 Category : Mathematics Languages : en Pages : 208
Book Description
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
Author: Vijay Gupta Publisher: Springer ISBN: 3319587951 Category : Mathematics Languages : en Pages : 193
Book Description
This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.
Author: Erling Størmer Publisher: Springer Science & Business Media ISBN: 3642343694 Category : Mathematics Languages : en Pages : 135
Book Description
This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.
Author: Charalambos D. Aliprantis Publisher: Springer Science & Business Media ISBN: 1402050089 Category : Computers Languages : en Pages : 389
Book Description
Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since publication of this book in 1985, the subject of positive operators and Riesz spaces has found practical applications in disciplines including social sciences and engineering. This book examines positive operators in the setting of Riesz spaces and Banach lattices, from both the algebraic and topological points of view.
Author: Farzaneh Jannat Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Approximation theory received much attention in the last century, and an intriguing area in this field is positive linear operators. This thesis is a literature survey on positive linear operators. We discuss some of the well-known examples of positive linear operators. Preserving $k$-monotonicity by positive linear operators is another interesting topic in this area. We are interested if $L_n(f;x)$ is $k$-monotone whenever function $f$ is $k$-monotone. For a sequence of positive linear operators $\{L_n(f;x)\}$, it is a natural question if this sequence converges to $f(x)$ and how fast is this convergence. We study the saturation of these operators. Usually, there is a relation between the rate of convergence and the smoothness of the function being approximated. If increasing smoothness of functions does not result in the increase of the degree of approximation, this phenomenon is called saturation. We discuss iteration of general positive linear operators and give numerical examples.
Author: Vijay Gupta Publisher: Springer ISBN: 3030194558 Category : Mathematics Languages : en Pages : 96
Book Description
This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.
Author: Vladimir Ya. Eiderman Publisher: Springer Science & Business Media ISBN: 3764373407 Category : Mathematics Languages : en Pages : 225
Book Description
This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.
Author: Radu Paltanea
Author: Radu Paltanea
Author: Mark Aleksandrovich Krasnoselʹskiĭ
Author: Vijay Gupta
Author: Ronald A. De Vore
Author: Erling Størmer
Author: Charalambos D. Aliprantis
Author: Ronald A. De Vore
Author: Farzaneh Jannat
Author: Vijay Gupta
Author: Vladimir Ya. Eiderman