Linear And Nonlinear Non Fredholm Operators
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Linear And Nonlinear Non Fredholm Operators
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Author : Messoud Efendiev
language : en
Publisher: Springer Nature
Release Date : 2023-02-04
Linear And Nonlinear Non Fredholm Operators written by Messoud Efendiev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-04 with Mathematics categories.
This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics. First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear – nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of “stagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood. Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local – nonlocal diffusion as well as terms for transport and nonlinear interactions.
Analysis Of Pseudo Differential Operators
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Author : Shahla Molahajloo
language : en
Publisher: Springer
Release Date : 2019-05-08
Analysis Of Pseudo Differential Operators written by Shahla Molahajloo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-08 with Mathematics categories.
This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.
Applied Functional Analysis
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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Functional Analysis written by Eberhard Zeidler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question as quickly as possible. Here, one walks directly on the main road and does not wander into all the nice and interesting side roads. The present book is based on the second approach. It is addressed to undergraduate and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems that are related to our real world and that have played an important role in the history of mathematics. The reader should sense that the theory is being developed, not simply for its own sake, but for the effective solution of concrete problems. viii Preface This introduction to functional analysis is divided into the following two parts: Part I: Applications to mathematical physics (the present AMS Vol. 108); Part II: Main principles and their applications (AMS Vol. 109).
Regularity And Stochasticity Of Nonlinear Dynamical Systems
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Author : Dimitri Volchenkov
language : en
Publisher: Springer
Release Date : 2017-06-24
Regularity And Stochasticity Of Nonlinear Dynamical Systems written by Dimitri Volchenkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-24 with Technology & Engineering categories.
This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.
Mathematical Methods In Modern Complexity Science
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Author : Dimitri Volchenkov
language : en
Publisher: Springer Nature
Release Date : 2022-03-14
Mathematical Methods In Modern Complexity Science written by Dimitri Volchenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-14 with Science categories.
This book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic differential equations, synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems
Nonlinearity And Functional Analysis
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Author : Melvyn S. Berger
language : en
Publisher: Academic Press
Release Date : 1977-10-27
Nonlinearity And Functional Analysis written by Melvyn S. Berger and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-10-27 with Mathematics categories.
Nonlinearity and Functional Analysis is a collection of lectures that aim to present a systematic description of fundamental nonlinear results and their applicability to a variety of concrete problems taken from various fields of mathematical analysis. For decades, great mathematical interest has focused on problems associated with linear operators and the extension of the well-known results of linear algebra to an infinite-dimensional context. This interest has been crowned with deep insights, and the substantial theory that has been developed has had a profound influence throughout the mathematical sciences. This volume comprises six chapters and begins by presenting some background material, such as differential-geometric sources, sources in mathematical physics, and sources from the calculus of variations, before delving into the subject of nonlinear operators. The following chapters then discuss local analysis of a single mapping and parameter dependent perturbation phenomena before going into analysis in the large. The final chapters conclude the collection with a discussion of global theories for general nonlinear operators and critical point theory for gradient mappings. This book will be of interest to practitioners in the fields of mathematics and physics, and to those with interest in conventional linear functional analysis and ordinary and partial differential equations.
Algebraic Multiplicity Of Eigenvalues Of Linear Operators
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Author : Julián López-Gómez
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-09
Algebraic Multiplicity Of Eigenvalues Of Linear Operators written by Julián López-Gómez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-09 with Mathematics categories.
This book brings together all available results about the theory of algebraic multiplicities. It first offers a classic course on finite-dimensional spectral theory and then presents the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families. Coverage next transfers these results from linear to nonlinear analysis.
Pseudo Differential Operators Groups Geometry And Applications
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Author : M. W. Wong
language : en
Publisher: Birkhäuser
Release Date : 2017-01-20
Pseudo Differential Operators Groups Geometry And Applications written by M. W. Wong and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-20 with Mathematics categories.
This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.
Topological Methods In Nonlinear Functional Analysis
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Author : Sankatha Prasad Singh
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Topological Methods In Nonlinear Functional Analysis written by Sankatha Prasad Singh and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Covers the proceedings of the session on Fixed Point Theory and Applications held at the University of Toronto, August 21-26, 1982. This work presents theorems on the existence of fixed points of nonexpansive mappings and the convergence of the sequence of iterates of nonexpansive and quasi-nonexpansive mappings.
Traces And Determinants Of Linear Operators
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Author : Israel Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Traces And Determinants Of Linear Operators written by Israel Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The authors initially planned to write an article describing the origins and devel opments of the theory of Fredholm operators and to present their recollections of this topic. We started to read again classical papers and we were sidetracked by the literature concerned with the theory and applications of traces and determi nants of infinite matrices and integral operators. We were especially impressed by the papers of Poincare, von Koch, Fredholm, Hilbert and Carleman, as well as F. Riesz's book on infinite systems of linear equations. Consequently our plans were changed and we decided to write a paper on the history of determinants of infi nite matrices and operators. During the preparation of our paper we realized that many mathematical questions had to be answered in order to gain a more com plete understanding of the subject. So, we changed our plans again and decided to present the subject in a more advanced form which would satisfy our new require ments. This whole process took between four and five years of challenging, but enjoyable work. This entailed the study of the appropriate relatively recent results of Grothendieck, Ruston, Pietsch, Hermann Konig and others. After the papers [GGK1] and [GGK2] were published, we saw that the written material could serve as the basis of a book.