Perturbation theory for linear operators - Info and Reading Options

"Perturbation theory for linear operators" Table Of Contents:

• 1- Introduction
• 2- Operator Theory In Finite-Dimensional Vector Spaces
• 3- Vector Spaces And Normed Vector Spaces
• 4- Basic Notions
• 5- Bases
• 6- Linear Manifolds
• 7- Convergence And Norms
• 8- Topological Notions In A Normed Space
• 9- Infinite Series Of Vectors
• 10- Vector-Valued Functions
• 11- Linear Forms And The Adjoint Space
• 12- Linear Forms
• 13- The Adjoint Space
• 14- The Adjoint Basis
• 15- The Adjoint Space Of A Normed Space
• 16- The Convexity Of Balls
• 17- The Second Adjoint Space
• 18- Linear Operators
• 19- Definitions. Matrix Representations
• 20- Linear Operations On Operators
• 21- The Algebra Of Linear Operators
• 22- Projections. Nilpotents
• 23- Invariance. Decomposition
• 24- The Adjoint Operator
• 25- Analysis With Operators
• 26- Convergence And Norms For Operators
• 27- The Norm Of T^n
• 28- Examples Of Norms
• 29- Infinite Series Of Operators
• 30- Operator-Valued Functions
• 31- Pairs Of Projections
• 32- The Eigenvalue Problem
• 33- Definitions
• 34- The Resolvent
• 35- Singularities Of The Resolvent
• 36- The Canonical Form Of An Operator
• 37- The Adjoint Problem
• 38- Functions Of An Operator
• 39- Similarity Transformations
• 40- Operators In Unitary Spaces
• 41- Unitary Spaces
• 42- The Adjoint Space
• 43- Orthonormal Families
• 44- Linear Operators
• 45- Symmetric Forms And Symmetric Operators
• 46- Unitary, Isometric And Normal Operators
• 47- Projections
• 48- Pairs Of Projections
• 49- The Eigenvalue Problem
• 50- The Minimax Principle
• 51- Perturbation Theory In A Finite-Dimensional Space
• 52- Analytic Perturbation Of Eigenvalues
• 53- The Problem
• 54- Singularities Of The Eigenvalues
• 55- Perturbation Of The Resolvent
• 56- Perturbation Of The Eigenprojections
• 57- Singularities Of The Eigenprojections
• 58- Remarks And Examples
• 59- The Case Of T(x) Linear In x
• 60- Summary
• 61- Perturbation Series
• 62- The Total Projection For The λ-Group
• 63- The Weighted Mean Of Eigenvalues
• 64- The Reduction Process
• 65- Formulas For Higher Approximations
• 66- A Theorem Of Motzkin-Tausky
• 67- The Ranks Of The Coefficients Of The Perturbation Series
• 68- Convergence Radii And Error Estimates
• 69- Simple Estimates
• 70- The Method Of Majorizing Series
• 71- Estimates On Eigenvectors
• 72- Further Error Estimates
• 73- The Special Case Of A Normal Unperturbed Operator
• 74- The Enumerative Method
• 75- Similarity Transformations Of The Eigenspaces And Eigenvectors
• 76- Eigenvectors
• 77- Transformation Functions
• 78- Solution Of The Differential Equation
• 79- The Transformation Function And The Reduction Process
• 80- Simultaneous Transformation For Several Projections
• 81- Diagonalization Of A Holomorphic Matrix Function
• 82- Non-Analytic Perturbations
• 83- Continuity Of The Eigenvalues And The Total Projection
• 84- The Numbering Of The Eigenvalues
• 85- Continuity Of The Eigenspaces And Eigenvectors
• 86- Differentiability At A Point
• 87- Differentiability In An Interval
• 88- Asymptotic Expansion Of The Eigenvalues And Eigenvectors
• 89- Operators Depending On Several Parameters
• 90- The Eigenvalues As Functions Of The Operator
• 91- Perturbation Of Symmetric Operators
• 92- Analytic Perturbation Of Symmetric Operators
• 93- Orthonormal Families Of Eigenvectors
• 94- Continuity And Differentiability
• 95- The Eigenvalues As Functions Of The Symmetric Operator
• 96- Applications: A Theorem Of Lidskii
• 97- Introduction To The Theory Of Operators In Banach Spaces
• 98- Banach Spaces
• 99- Normed Spaces
• 100- Banach Spaces
• 101- Linear Forms
• 102- The Adjoint Space
• 103- The Principle Of Uniform Boundedness
• 104- Weak Convergence
• 105- Weak* Convergence
• 106- The Quotient Space
• 107- Linear Operators In Banach Spaces
• 108- Linear Operators: The Domain And Range
• 109- Continuity And Boundedness
• 110- Ordinary Differential Operators Of Second Order
• 111- Bounded Operators
• 112- The Space Of Bounded Operators
• 113- The Operator Algebra B(X)
• 114- The Adjoint Operator
• 115- Projections
• 116- Compact Operators
• 117- Definition
• 118- The Space Of Compact Operators
• 119- Degenerate Operators: The Trace And Determinant
• 120- Closed Operators
• 121- Remarks On Unbounded Operators
• 122- Closed Operators
• 123- Closable Operators
• 124- The Closed Graph Theorem
• 125- The Adjoint Operator
• 126- Commutativity And Decomposition
• 127- Resolvents And Spectra
• 128- Definitions
• 129- The Spectra Of Bounded Operators
• 130- The Point At Infinity
• 131- Separation Of The Spectrum
• 132- Isolated Eigenvalues
• 133- The Resolvent of the Adjoint
• 134- The Spectra of Compact Operators
• 135- Operators with Compact Resolvent
• 136- Stability Theorems
• 137- Stability of Closedness and Bounded Invertibility
• 138- Stability of Closedness Under Relatively Bounded Perturbation
• 139- Examples of Relative Boundedness
• 140- Relative Compactness and a Stability Theorem
• 141- Stability of Bounded Invertibility
• 142- Generalized Convergence of Closed Operators
• 143- The Gap Between Subspaces
• 144- The Gap and the Dimension
• 145- Duality
• 146- The Gap Between Closed Operators
• 147- Further Results on the Stability of Bounded Invertibility
• 148- Generalized Convergence
• 149- Perturbation of the Spectrum
• 150- Upper Semicontinuity of the Spectrum
• 151- Lower Semi-Discontinuity of the Spectrum
• 152- Continuity and Analyticity of the Resolvent
• 153- Semicontinuity of Separated Parts of the Spectrum
• 154- Continuity of a Finite System of Eigenvalues
• 155- Change of the Spectrum Under Relatively Bounded Perturbation
• 156- Simultaneous Consideration of an Infinite Number of Eigenvalues
• 157- An Application to Banach Algebras: Wiener's Theorem
• 158- Pairs of Closed Linear Manifolds
• 159- Definitions
• 160- Duality
• 161- Regular Pairs of Closed Linear Manifolds
• 162- The Approximate Nullity and Deficiency
• 163- Stability Theorems
• 164- Stability Theorems for Semi-Fredholm Operators
• 165- The Nullity, Deficiency and Index of an Operator
• 166- The General Stability Theorem
• 167- Other Stability Theorems
• 168- Isolated Eigenvalues
• 169- Another Form of the Stability Theorem
• 170- Structure of the Spectrum of a Closed Operator
• 171- Degenerate Perturbations
• 172- The Weinstein-Aronszajn Determinants
• 173- The W-A Formulas
• 174- Proof of the W-A Formulas
• 175- Conditions Excluding the Singular Case
• 176- Operators in Hilbert Spaces
• 177- Hilbert Space
• 178- Basic Notions
• 179- Complete Orthonormal Families
• 180- Bounded Operators in Hilbert Spaces
• 181- Bounded Operators and Their Adjoints
• 182- Unitary and Isometric Operators
• 183- Compact Operators
• 184- The Schmidt Class
• 185- Perturbation of Orthonormal Families
• 186- Unbounded Operators in Hilbert Spaces
• 187- General Remarks
• 188- The Numerical Range
• 189- Symmetric Operators
• 190- The Spectra of Symmetric Operators
• 191- The Resolvents and Spectra of Selfadjoint Operators
• 192- Second-Order Ordinary Differential Operators
• 193- The Operators T*T
• 194- Normal Operators
• 195- Reduction of Symmetric Operators
• 196- Semibounded and Accretive Operators
• 197- The Square Root of an m-Accretive Operator
• 198- Perturbation of Selfadjoint Operators
• 199- Stability of Selfadjointness
• 200- The Case of Relative Bound 1
• 201- Perturbation of the Spectrum
• 202- Semibounded Operators
• 203- Completeness of the Eigenprojections of Slightly Non-Selfadjoint Operators
• 204- The Schrödinger and Dirac Operators
• 205- Partial Differential Operators
• 206- The Laplacian in the Whole Space
• 207- The Schrödinger Operator with a Static Potential
• 208- The Dirac Operator
• 209- Sesquilinear Forms in Hilbert Spaces and Associated Operators
• 210- Sesquilinear and Quadratic Forms
• 211- Definitions
• 212- Semiboundedness
• 213- Closed Forms
• 214- Closable Forms
• 215- Forms Constructed from Sectorial Operators
• 216- Sums of Forms
• 217- Relative Boundedness for Forms and Operators
• 218- The Representation Theorems
• 219- The First Representation Theorem
• 220- Proof of the First Representation Theorem
• 221- The Friedrichs Extension
• 222- Other Examples for the Representation Theorem
• 223- Supplementary Remarks
• 224- The Second Representation Theorem
• 225- The Polar Decomposition of a Closed Operator
• 226- Perturbation of Sesquilinear Forms and the Associated Operators
• 227- The Real Part of an M-Sectorial Operator
• 228- Perturbation of an M-Sectorial Operator and Its Resolvent
• 229- Symmetric Unperturbed Operators
• 230- Pseudo-Friedrichs Extensions
• 231- Quadratic Forms and the Schrödinger Operators
• 232- Ordinary Differential Operators
• 233- The Dirichlet Form and the Laplace Operator
• 234- The Schrödinger Operators in R³
• 235- Bounded Regions
• 236- The Spectral Theorem and Perturbation of Spectral Families
• 237- Spectral Families
• 238- The Selfadjoint Operator Associated with a Spectral Family
• 239- The Spectral Theorem
• 240- Stability Theorems for the Spectral Family
• 241- Analytic Perturbation Theory
• 242- Analytic Families of Operators
• 243- Analyticity of Vector- and Operator-Valued Functions
• 244- Analyticity of a Family of Unbounded Operators
• 245- Separation of the Spectrum and Finite Systems of Eigenvalues
• 246- Remarks on Infinite Systems of Eigenvalues
• 247- Perturbation Series
• 248- A Holomorphic Family Related to a Degenerate Perturbation
• 249- Holomorphic Families of Type (A)
• 250- Definition
• 251- A Criterion for Type (A)
• 252- Remarks on Holomorphic Families of Type (A)
• 253- Convergence Radii and Error Estimates
• 254- Normal Unperturbed Operators
• 255- Selfadjoint Holomorphic Families
• 256- General Remarks
• 257- Continuation of the Eigenvalues
• 258- The Mathieu, Schrödinger, and Dirac Equations
• 259- Growth Rate of the Eigenvalues
• 260- Total Eigenvalues Considered Simultaneously
• 261- Holomorphic Families of Type (B)
• 262- Bounded-Holomorphic Families of Sesquilinear Forms
• 263- Holomorphic Families of Forms of Type (A) and Holomorphic Families of Operators of Type (B)
• 264- A Criterion for Type (B)
• 265- Holomorphic Families of Type (B₀)
• 266- The Relationship Between Holomorphic Families of Types (A) and (B)
• 267- Perturbation Series for Eigenvalues and Eigenprojections
• 268- Growth Rate of Eigenvalues and the Total System of Eigenvalues
• 269- Application to Differential Operators
• 270- The Two-Electron Problem
• 271- Further Problems of Analytic Perturbation Theory
• 272- Holomorphic Families of Type (C)
• 273- Analytic Perturbation of the Spectral Family
• 274- Analyticity of
• 275- Eigenvalue Problems in the Generalized Form
• 276- General Considerations
• 277- Perturbation Theory
• 278- Holomorphic Families of Type (A)
• 279- Holomorphic Families of Type (B)
• 280- Boundary Perturbation
• 281- Asymptotic Perturbation Theory
• 282- Strong Convergence in the Generalized Sense
• 283- Strong Convergence of the Resolvent
• 284- Generalized Strong Convergence and Spectra
• 285- Perturbation of Eigenvalues and Eigenvectors
• 286- Stable Eigenvalues
• 287- Asymptotic Expansions
• 288- Asymptotic Expansion of the Resolvent
• 289- Remarks on Asymptotic Expansions
• 290- Asymptotic Expansions of Isolated Eigenvalues and Eigenvectors
• 291- Further Asymptotic Expansions
• 292- Generalized Strong Convergence of Sectorial Operators
• 293- Convergence of a Sequence of Bounded Forms
• 294- Convergence of Sectorial Forms "From Above"
• 295- Nonincreasing Sequences of Symmetric Forms
• 296- Convergence from Below
• 297- Spectra of Converging Operators
• 298- Asymptotic Expansions for Sectorial Operators
• 299- The Problem. The Zeroth Approximation for the Resolvent
• 300- The 1/2-Order Approximation for the Resolvent
• 301- The First and Higher Order Approximations for the Resolvent
• 302- Asymptotic Expansions for Eigenvalues and Eigenvectors
• 303- Spectral Concentration
• 304- Unstable Eigenvalues
• 305- Spectral Concentration
• 306- Pseudo-Eigenvectors and Spectral Concentration
• 307- Asymptotic Expansions
• 308- Perturbation Theory for Semigroups of Operators
• 309- One-Parameter Semigroups and Groups of Operators
• 310- The Problem
• 311- Definition of the Exponential Function
• 312- Properties of the Exponential Function
• 313- Bounded and Quasi-Bounded Semigroups
• 314- Solution of the Inhomogeneous Differential Equation
• 315- Holomorphic Semigroups
• 316- The Inhomogeneous Differential Equation for a Holomorphic Semigroup
• 317- Perturbation of Semigroups
• 318- Analytic Perturbation of Quasi-Bounded Semigroups
• 319- Analytic Perturbation of Holomorphic Semigroups
• 320- Perturbation of Contraction Semigroups
• 321- Convergence of Quasi-Bounded Semigroups in a Restricted Sense
• 322- Strong Convergence of Quasi-Bounded Semigroups
• 323- Asymptotic Perturbation of Semigroups
• 324- Approximation by Discrete Semigroups
• 325- Discrete Semigroups
• 326- Approximation of a Continuous Semigroup by Discrete Semigroups
• 327- Approximation Theorems
• 328- Variation of the Space
• 329- Perturbation of Continuous Spectra and Unitary Equivalence
• 330- The Continuous Spectrum of a Selfadjoint Operator
• 331- The Point and Continuous Spectra
• 332- The Absolutely Continuous and Singular Spectra
• 333- The Trace Class
• 334- The Trace and Determinant
• 335- Perturbation of Continuous Spectra
• 336- A Theorem of Weyl-Von Neumann
• 337- A Generalization
• 338- Wave Operators and the Stability of Absolutely Continuous Spectra
• 339- Introduction
• 340- Generalized Wave Operators
• 341- A Sufficient Condition for the Existence of the Wave Operator
• 342- An Application to Potential Scattering
• 343- Existence and Completeness of Wave Operators
• 344- Perturbations of Rank One (Special Case)
• 345- Perturbations of Rank One (General Case)
• 346- Perturbations of the Trace Class
• 347- Wave Operators for Functions of Operators
• 348- Strengthening of the Existence Theorems
• 349- Dependence of W+ (H₂, H₁) on H₁ and H₂
• 350- A Stationary Method
• 351- Introduction
• 352- The I Operations
• 353- Equivalence with the Time-Dependent Theory
• 354- The I Operations on Degenerate Operators
• 355- Solution of the Integral Equation for Rank A = 1
• 356- Solution of the Integral Equation for a Degenerate A
• 357- Application to Differential Operators
• 358- Supplementary Notes
• 359- Bibliography
• 360- Articles
• 361- Books and Monographs
• 362- Supplementary Bibliography
• 363- Articles
• 364- Notation Index
• 365- Author Index
• 366- Subject Index

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