Applications Of Q Calculus In Operator Theory

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Applications of q-Calculus in Operator Theory

Author : Ali Aral,Vijay Gupta,Ravi P. Agarwal
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 41,6 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9781461469469

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Applications of q-Calculus in Operator Theory by Ali Aral,Vijay Gupta,Ravi P. Agarwal Pdf

The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. ​​This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain​ forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.

Applications of Functional Analysis and Operator Theory

Author : V. Hutson,J. Pym,M. Cloud
Publisher : Elsevier
Page : 442 pages
File Size : 55,8 Mb
Release : 2005-02-08
Category : Mathematics
ISBN : 9780080527314

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Applications of Functional Analysis and Operator Theory by V. Hutson,J. Pym,M. Cloud Pdf

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results Introduces each new topic with a clear, concise explanation Includes numerous examples linking fundamental principles with applications Solidifies the reader's understanding with numerous end-of-chapter problems

Operator Theory and Its Applications

Author : Alexander G. Ramm,P. N. Shivakumar,Abraham Vilgelmovich Strauss
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 46,7 Mb
Release : 2000
Category : Operator theory
ISBN : 9780821819906

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Operator Theory and Its Applications by Alexander G. Ramm,P. N. Shivakumar,Abraham Vilgelmovich Strauss Pdf

Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.

Current Trends in Operator Theory and its Applications

Author : Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman
Publisher : Birkhäuser
Page : 604 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878814

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Current Trends in Operator Theory and its Applications by Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman Pdf

Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.

Topics in Operator Theory

Author : Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 46,8 Mb
Release : 2011-02-09
Category : Mathematics
ISBN : 9783034601580

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Topics in Operator Theory by Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky Pdf

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Systems, Approximation, Singular Integral Operators, and Related Topics

Author : Alexander A. Borichev,Nikolai K. Nikolski
Publisher : Birkhäuser
Page : 536 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783034883627

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Systems, Approximation, Singular Integral Operators, and Related Topics by Alexander A. Borichev,Nikolai K. Nikolski Pdf

This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.

The Extended Field of Operator Theory

Author : Michael A. Dritschel
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 47,8 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9783764379803

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The Extended Field of Operator Theory by Michael A. Dritschel Pdf

This volume contains contributions originating from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Newcastle upon Tyne in July 2004. The articles expertly cover a broad range of material at the cutting edge of functional analysis and its applications. The works are written by world authorities in their specialities.

New Results in Operator Theory and Its Applications

Author : Israel Gohberg,Yuri I. Lyubich
Publisher : Birkhäuser
Page : 269 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889100

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New Results in Operator Theory and Its Applications by Israel Gohberg,Yuri I. Lyubich Pdf

This volume is dedicated to the memory of Israel Glazman, an outstanding personality and distinguished mathematician, the author of many remarkable papers and books in operator theory and its applications. The present book opens with an essay devoted to Glazman's life and scientific achievements. It focusses on the areas of his unusually wide interests and consists of 18 mathematical papers in spectral theory of differential operators and linear operators in Hilbert and Banach spaces, analytic operator functions, ordinary and partial differential equations, functional equations, mathematical physics, nonlinear functional analysis, approximation theory and optimization, and mathematical statistics. The book gives a picture of the current state of some important problems in areas of operator theory and its applications and will be of interest to a wide group of researchers working in pure and applied mathematics.

Noncommutative Analysis, Operator Theory and Applications

Author : Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot
Publisher : Birkhäuser
Page : 283 pages
File Size : 40,8 Mb
Release : 2016-06-30
Category : Mathematics
ISBN : 9783319291161

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Noncommutative Analysis, Operator Theory and Applications by Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot Pdf

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

Recent Advances in Operator Theory and Applications

Author : Tsuyoshi Ando,Il Bong Jung,Woo Young Lee
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 51,6 Mb
Release : 2008-12-19
Category : Mathematics
ISBN : 9783764388935

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Recent Advances in Operator Theory and Applications by Tsuyoshi Ando,Il Bong Jung,Woo Young Lee Pdf

Contains the proceedings of the International Workshop on Operator Theory and Applications (IWOTA 2006) held at Seoul National University, Seoul, Korea, from July 31 to August 3, 2006. This volume contains sixteen research papers which reflect developments in operator theory and applications.

Mathematical Analysis and its Applications

Author : P. N. Agrawal,R. N. Mohapatra,Uaday Singh,H. M. Srivastava
Publisher : Springer
Page : 764 pages
File Size : 52,7 Mb
Release : 2015-08-22
Category : Mathematics
ISBN : 9788132224853

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Mathematical Analysis and its Applications by P. N. Agrawal,R. N. Mohapatra,Uaday Singh,H. M. Srivastava Pdf

This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical analysis and at promoting the exchange of ideas in various applications of mathematics in engineering, physics and biology. This conference encourages international collaboration and provides young researchers an opportunity to learn about the current state of the research in their respective fields.

Mathematical Analysis and Analytic Number Theory 2019

Author : Rekha Srivastava
Publisher : MDPI
Page : 318 pages
File Size : 52,6 Mb
Release : 2021-04-06
Category : Mathematics
ISBN : 9783036500324

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Mathematical Analysis and Analytic Number Theory 2019 by Rekha Srivastava Pdf

This volume is a collection of investigations involving the theory and applications of the various tools and techniques of mathematical analysis and analytic number theory, which are remarkably widespread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. It contains invited and welcome original as well as review-cum-expository research articles dealing with recent and new developments on the topics of mathematical analysis and analytic number theory as well as their multidisciplinary applications.

Operator Theory in Different Settings and Related Applications

Author : Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov
Publisher : Birkhäuser
Page : 309 pages
File Size : 55,5 Mb
Release : 2018-03-28
Category : Mathematics
ISBN : 9783319625270

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Operator Theory in Different Settings and Related Applications by Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov Pdf

This book provides a selection of reports and survey articles on the latest research in the area of single and multivariable operator theory and related fields. The latter include singular integral equations, ordinary and partial differential equations, complex analysis, numerical linear algebra, and real algebraic geometry – all of which were among the topics presented at the 26th International Workshop in Operator Theory and its Applications, held in Tbilisi, Georgia, in the summer of 2015. Moreover, the volume includes three special commemorative articles. One of them is dedicated to the memory of Leiba Rodman, another to Murray Marshall, and a third to Boris Khvedelidze, an outstanding Georgian mathematician and one of the founding fathers of the theory of singular integral equations. The book will be of interest to a broad range of mathematicians, from graduate students to researchers, whose primary interests lie in operator theory, complex analysis and applications, as well as specialists in mathematical physics.

Recent Advances in Operator Theory, Operator Algebras, and their Applications

Author : Dumitru Gaspar,Israel Gohberg,Dan Timotin,Florian H. Vasilescu,Laszlo Zsido
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 43,6 Mb
Release : 2004-11-22
Category : Mathematics
ISBN : 3764371277

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Recent Advances in Operator Theory, Operator Algebras, and their Applications by Dumitru Gaspar,Israel Gohberg,Dan Timotin,Florian H. Vasilescu,Laszlo Zsido Pdf

This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.

A Comprehensive Treatment of q-Calculus

Author : Thomas Ernst
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 48,7 Mb
Release : 2012-09-08
Category : Mathematics
ISBN : 9783034804301

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A Comprehensive Treatment of q-Calculus by Thomas Ernst Pdf

To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.​