Operator Relations Characterizing Derivatives
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| Author | : Hermann König |
| Publisher | : Springer |
| Total Pages | : 193 |
| Release | : 2018-10-03 |
| Genre | : Mathematics |
| ISBN | : 3030002411 |
This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature. Major constructions or operations in analysis are often characterized by some elementary properties, relations or equations which they satisfy. The authors present recent results on the problem to what extent the derivative is characterized by equations such as the Leibniz rule or the Chain rule operator equation in Ck-spaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, Sturm-Liouville operators and the Laplacian motivate the study of certain "second-order" operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of non-degeneration. In their approach, operators are not required to be linear, and the authors also try to avoid continuity conditions. The Leibniz rule, the Chain rule and its extensions turn out to be stable under perturbations and relaxations of assumptions on the form of the operators. The results yield an algebraic understanding of first- and second-order differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operator-type structure behind the fundamental notion of the derivative and its relatives in analysis is discovered and explored. The book does not require any specific knowledge of functional equations. All needed results are presented and proven and the book is addressed to a general mathematical audience.
| Author | : Piotr Budzyński |
| Publisher | : Springer |
| Total Pages | : 189 |
| Release | : 2018-05-28 |
| Genre | : Mathematics |
| ISBN | : 3319740393 |
This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L2-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of unbounded weighted composition operators are characterized. The first-ever criteria for subnormality of unbounded weighted composition operators are provided and the subtle interplay between the classical moment problem, graph theory and the injectivity problem for weighted composition operators is revealed. The relationships between weighted composition operators and the corresponding multiplication and composition operators are investigated. The optimality of the obtained results is illustrated by a variety of examples, including those of discrete and continuous types. The book is primarily aimed at researchers in single or multivariable operator theory.
| Author | : Shib Sankar Ganguli |
| Publisher | : Elsevier |
| Total Pages | : 518 |
| Release | : 2023-10-27 |
| Genre | : Science |
| ISBN | : 032399718X |
Reservoir Characterization, Modeling and Quantitative Interpretation: Recent Workflows to Emerging Technologies offers a wide spectrum of reservoir characterization techniques and technologies, focusing on the latest breakthroughs and most efficient methodologies in hydrocarbon exploration and development. Topics covered include 4D seismic technologies, AVAz inversion, fracture characterization, multiscale imaging technologies, static and dynamic reservoir characterization, among others. The content is delivered through an inductive approach, which will help readers gain comprehensive insights on advanced practices and be able to relate them to other subareas of reservoir characterization, including CO2 storage and data-driven modeling. This will be especially useful for field scientists in collecting and analyzing field data, prospect evaluation, developing reservoir models, and adopting new technologies to mitigate exploration risk. They will be able to solve the practical and challenging problems faced in the field of reservoir characterization, as it will offer systematic industrial workflows covering every aspect of this branch of Earth Science, including subsurface geoscientific perspectives of carbon geosequestration. This resource is a 21st Century guide for exploration geologists, geoscience students at postgraduate level and above, and petrophysicists working in the oil and gas industry. - Covers the latest and most effective technologies in reservoir characterization, including Avo analysis, AVAz inversion, wave field separation and Machine Learning techniques - Provides a balanced blend of both theoretical and practical approaches for solving challenges in reservoir characterization - Includes detailed industry-standard practical workflows, along with code structures for algorithms and practice exercises
| Author | : Alexandre Almeida |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 389 |
| Release | : 2013-01-31 |
| Genre | : Mathematics |
| ISBN | : 3034805160 |
This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.
| Author | : Leo J. Grady |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 371 |
| Release | : 2010-07-23 |
| Genre | : Computers |
| ISBN | : 1849962901 |
This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.
| Author | : Zhiming Liu |
| Publisher | : Springer |
| Total Pages | : 574 |
| Release | : 2005-02-22 |
| Genre | : Computers |
| ISBN | : 3540318623 |
This book constitutes the thoroughly refereed postproceedings of the First International Colloquium on Theoretical Aspects of Computing, ICTAC 2004. The 34 revised full papers presented together with 4 invited contributions were carefully selected from 111 submissions during two rounds of reviewing and improvement. The papers are organized in topical sections on concurrent and distributed systems, model integration and theory unification, program reasoning and testing, verification, theories of programming and programming languages, real-time and co-design, and automata theory and logics.
| Author | : George Isac |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2008-05-21 |
| Genre | : Mathematics |
| ISBN | : 0387739882 |
This extremely useful book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. The text is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry and applied mathematics.
| Author | : Stefano Boccaletti |
| Publisher | : World Scientific |
| Total Pages | : 323 |
| Release | : 2001-03-09 |
| Genre | : Science |
| ISBN | : 9814491845 |
This book provides a comprehensive overview of the topics related to characterization, control and synchronization of complex spatiotemporal phenomena, from both a theoretical and an experimental point of view. It describes applications of these processes in applied mathematics, signal analysis, nonlinear optics, fluid dynamics, chemical reactions, electronic circuits, etc.
| Author | : Wen Chen |
| Publisher | : Springer Nature |
| Total Pages | : 381 |
| Release | : 2022-02-26 |
| Genre | : Mathematics |
| ISBN | : 9811688028 |
This textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.
| Author | : Swanhild Bernstein |
| Publisher | : Springer Nature |
| Total Pages | : 509 |
| Release | : 2019-10-15 |
| Genre | : Mathematics |
| ISBN | : 3030238547 |
Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
