Dynamics Of Linear Operators
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Author |
: Frédéric Bayart |
Publisher |
: Cambridge University Press |
Total Pages |
: 352 |
Release |
: 2009-06-04 |
ISBN-10 |
: 9780521514965 |
ISBN-13 |
: 0521514967 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Dynamics of Linear Operators by : Frédéric Bayart
The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
Author |
: Etienne Matheron |
Publisher |
: |
Total Pages |
: |
Release |
: 2005 |
ISBN-10 |
: OCLC:741249489 |
ISBN-13 |
: |
Rating |
: 4/5 (89 Downloads) |
Synopsis DYNAMICS OF LINEAR OPERATORS. by : Etienne Matheron
Author |
: Martina Maiuriello |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2022 |
ISBN-10 |
: 9791221801316 |
ISBN-13 |
: |
Rating |
: 4/5 (16 Downloads) |
Synopsis Dynamics of Linear Operators by : Martina Maiuriello
Author |
: Karl-G. Grosse-Erdmann |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 391 |
Release |
: 2011-08-24 |
ISBN-10 |
: 9781447121701 |
ISBN-13 |
: 1447121708 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Linear Chaos by : Karl-G. Grosse-Erdmann
It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.
Author |
: Joel H.. Shapiro |
Publisher |
: |
Total Pages |
: 61 |
Release |
: 2001 |
ISBN-10 |
: OCLC:1302754550 |
ISBN-13 |
: |
Rating |
: 4/5 (50 Downloads) |
Synopsis Notes on the Dynamics of Linear Operators by : Joel H.. Shapiro
Author |
: David Applebaum |
Publisher |
: Cambridge University Press |
Total Pages |
: 235 |
Release |
: 2019-08-15 |
ISBN-10 |
: 9781108483094 |
ISBN-13 |
: 1108483097 |
Rating |
: 4/5 (94 Downloads) |
Synopsis Semigroups of Linear Operators by : David Applebaum
Provides a graduate-level introduction to the theory of semigroups of operators.
Author |
: Jonathan R. Partington |
Publisher |
: Cambridge University Press |
Total Pages |
: 184 |
Release |
: 2004-03-15 |
ISBN-10 |
: 0521546192 |
ISBN-13 |
: 9780521546195 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Linear Operators and Linear Systems by : Jonathan R. Partington
Publisher Description
Author |
: S. Banach |
Publisher |
: Elsevier |
Total Pages |
: 249 |
Release |
: 1987-03-01 |
ISBN-10 |
: 9780080887203 |
ISBN-13 |
: 0080887201 |
Rating |
: 4/5 (03 Downloads) |
Synopsis Theory of Linear Operations by : S. Banach
This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.
Author |
: Harold T. Davis |
Publisher |
: Myers Press |
Total Pages |
: 648 |
Release |
: 2008-11 |
ISBN-10 |
: 9781443731492 |
ISBN-13 |
: 1443731498 |
Rating |
: 4/5 (92 Downloads) |
Synopsis The Theory of Linear Operators by : Harold T. Davis
THE THEORY OF LINEAR OPERATORS FROM THE STANDPOINT OF DIFFEREN TIAL EQUATIONS OF INFINITE ORDER By HAROLD T. DAVIS INDIANA UNIVERSITY AND THE COWLES COMMISSION FOR RESEARCH IN ECONOMICS THE PRINCIPIA PRESS Bloommgton, Indiana 1936 MONOGRAPH OF THE WATERMAN INSTITUTE OF INDIANA UNIVERSITY CONTRIBUTION NO. 72 THE THEORY OF LINEAR OPERATORS To Agnes, who endured so patiently the writing of it, this boo is affectionately dedicated. TABLE OF CONTENTS CHAPTER I LINEAR OPERATORS 1. The Nature of Operators ------------1 2. Definition of an Operator -----.--3 3. A Classification of Operational Methods --------7 4. The Formal Theory of Operators ----------g 5. Generalized Integration and Differentiation - - 16 6. Differential and Integral Equations of Infinite Order -----23 7. The Generatrix Calculus - - 28 8. The Heaviside Operational Calculus ---------34 9. The Theory of Functionals ------------33 10. The Calculus of Forms in Infinitely Many Variables -----4 CHAPTER II PARTICULAR OPERATORS 1. Introduction ----------------51 2. Polynomial Operators --------53 3. The Fourier Definition of an Operator ---------53 4. The Operational Symbol of von Neumann and Stone -----57 5. The Operator as a Laplace Transform ---------59 6. Polar Operators ...-60 7. Branch Point Operators ------------64 8. Note on the Complementary Function ---------70 9. Riemanns Theory - .--.--72 10. Functions Permutable with Unity ----------76 11. Logarithmic Operators ------------78 12. Special Operators --------------85 13. The General Analytic Operator ----------99 14. The Differential Operator of Infinite Order -------100 15. Differential Operators as a Cauchy Integral -------103 16. The Generatrix of Differential Operators--------104 17. Five Operators of Analysis ------------105 CHAPTER III THE THEORY OF LINEAR SYSTEMS OF EQUATIONS 1. Preliminary Remarks -------------108 2. Types of Matrices --------------109 3. The Convergence of an Infinite Determinant -------114 4. The Upper Bound of a Determinant. Hadamards Theorem - - 116 5. Determinants which do not Vanish - - - - - - - - - 123 6. The Method of the Liouville-Neumann Series -------126 7. The Method of Segments ------------130 8. Applications of the Method of Segments. --------132 9. The Hilbert Theory of Linear Equations in an Infinite Number of Variables - - - - 137 10. Extension of the Foregoing Theory to Holder Space 149 vii Vlll THE THEORY OF LINEAR OPERATORS CHAPTER IV OPERATIONAL MULTIPLICATION AND INVERSION 1. Algebra and Operators -------.. --153 2. The Generalized Formula of Leibnitz ---------154 3. Bourlets Operational Product --. 155 4. The Algebra of Functions of Composition --------159 5. Selected Problems in the Algebra of Permutable Functions - - - - 164 G. The Calculation of a Function Permutable with a Given Function - 166 7. The Transformation of Peres -----------171 8. The Permutability of Functions Permutable with a Given Function - 173 9. Permutable Functions of Second Kind - --176 10. The Inversion of Operators Bourlets Theory ------177 It. The Method of Successive Substitutions --------181 12. Some Further Properties of the Resolvent Generatrix - 185 13. The Inversion of Operators by Infinite Differentiation - 188 14. The Permutability of Linear PilYeiential Operators -----190 15. A Class of Non-permutable Operators ---------194 16. Special Examples Illustrating the Application of Operational Processes 200 CHAPTER V GRADESDEFINED BY SPECIAL OPERATORS 1. Definition ----------------211 2. The Grade of an Unlimitedly Differentiable Function - 212 3. Functions of Finite Grade ------------215 4. Asymptotic Expansions --- 222 5. The Summability of Differential Operators with Constant Coefficients 230 6. The Summability of Operators of Laplace Type ------235 CHAPTER VI DIFFERENTIAL EQUATIONS OF INFINITE ORDER WITH CONSTANT COEFFICIENTS 1. Introduction ---------------238 2. Expansion of the Resolvent Generatrix --------239 3. The Method of Cauchy-Bromwich ----------250 4...
Author |
: H. Ted Davis |
Publisher |
: Elsevier |
Total Pages |
: 561 |
Release |
: 2000-07-12 |
ISBN-10 |
: 9780080510248 |
ISBN-13 |
: 0080510248 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Linear Algebra and Linear Operators in Engineering by : H. Ted Davis
Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Numerous examples, problems, and illustrations highlight applications from all over engineering and the physical sciences. Also included are several numerical applications, complete with Mathematica solutions and code, giving the student a "hands-on" introduction to numerical analysis. Linear Algebra and Linear Operators in Engineering is ideally suited as the main text of an introductory graduate course, and is a fine instrument for self-study or as a general reference for those applying mathematics. - Contains numerous Mathematica examples complete with full code and solutions - Provides complete numerical algorithms for solving linear and nonlinear problems - Spans elementary notions to the functional theory of linear integral and differential equations - Includes over 130 examples, illustrations, and exercises and over 220 problems ranging from basic concepts to challenging applications - Presents real-life applications from chemical, mechanical, and electrical engineering and the physical sciences