Progress in Approximation Theory and Applicable Complex Analysis PDF Download

Author: Narendra Kumar Govil
Publisher: Springer
ISBN: 331949242X
Category : Mathematics
Languages : en
Pages : 541

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Book Description
Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.

Author: Themistocles M. Rassias
Publisher: Springer Nature
ISBN: 3030606228
Category : Mathematics
Languages : en
Pages : 546

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Book Description
This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Author: Javad Mashreghi
Publisher: Springer
ISBN: 1493975439
Category : Mathematics
Languages : en
Pages : 277

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Book Description
The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.

Author: Gerd Baumann
Publisher: Springer Nature
ISBN: 303049716X
Category : Mathematics
Languages : en
Pages : 411

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Book Description
This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.

Author: Robert B. Gardner
Publisher: Academic Press
ISBN: 012812007X
Category : Mathematics
Languages : en
Pages : 444

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Book Description
Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. - Applies Markov-Bernstein-type inequalities to any problem where derivative estimates are necessary - Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions, and entire functions of exponential type - Contains exhaustive references with more than five hundred citations to articles and books - Features methods to solve inverse problems across approximation theory - Includes open problems for further research

Author: Manoj Kumar Patel
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111313638
Category : Mathematics
Languages : en
Pages : 512

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Book Description
This volume documents the contributions presented at The ICRTMPCS II International Conference on Advances in Mathematical and Computational Sciences. Entries focus on modern trends and techniques in branches of pure and applied mathematics, statistics, and computer science. Highlighting applications in coding theory, cryptography, graph theory, fuzzy theory, variance analysis, data analysis, and sampling theory.

Author: Nicholas J. Daras
Publisher: Springer Nature
ISBN: 3030841227
Category : Mathematics
Languages : en
Pages : 934

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Book Description
In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Author: Andreas Defant
Publisher: Cambridge University Press
ISBN: 1108476716
Category : Mathematics
Languages : en
Pages : 709

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Book Description
Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.

Author: Bicheng Yang
Publisher: World Scientific
ISBN: 9811267111
Category : Mathematics
Languages : en
Pages : 203

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Book Description
Hilbert-type inequalities, including Hilbert's inequalities proved in 1908, Hardy-Hilbert-type inequalities proved in 1934, and Yang-Hilbert-type inequalities first proved around 1998, play an important role in analysis and its applications. These inequalities are mainly divided in three classes: integral, discrete and half-discrete. During the last twenty years, there have been many research advances on Hilbert-type inequalities, and especially on Yang-Hilbert-type inequalities.In the present monograph, applying weight functions, the idea of parametrization as well as techniques of real analysis and functional analysis, we prove some new Hilbert-type integral inequalities as well as their reverses with parameters. These inequalities constitute extensions of the well-known Hardy-Hilbert integral inequality. The equivalent forms and some equivalent statements of the best possible constant factors associated with several parameters are considered. Furthermore, we also obtain the operator expressions with the norm and some particular inequalities involving the Riemann-zeta function and the Hurwitz-zeta function. In the form of applications, by means of the beta function and the gamma function, we use the extended Hardy-Hilbert integral inequalities to consider several Hilbert-type integral inequalities involving derivative functions and upper limit functions. In the last chapter, we consider the case of Hardy-type integral inequalities. The lemmas and theorems within provide an extensive account of these kinds of integral inequalities and operators.Efforts have been made for this monograph hopefully to be useful, especially to graduate students of mathematics, physics and engineering, as well as researchers in these domains.

Author: Ilia Binder
Publisher: Springer Nature
ISBN: 3031392701
Category : Mathematics
Languages : en
Pages : 487

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Book Description
The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.