Functional Analysis
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패키지
북카드
작가정보
저자(글) Lax, Peter D.
목차
Foreword p. xvii Linear Spaces p. 1 Linear Maps p. 8 Algebra of linear maps p. 8 Index of a linear map p. 12 The Hahn-Banach Theorem p. 19 The extension theorem p. 19 Geometric Hahn-Banach theorem p. 21 Extensions of the Hahn-Banach theorem p. 24 Applications of the Hahn-Banach theorem p. 29 Extension of positive linear functionals p. 29 Banach limits p. 31 Finitely additive invariant set functions p. 33 Historical note p. 34 Normed Linear Spaces p. 36 Norms p. 36 Noncompactness of the unit ball p. 43 Isometries p. 47 Hilbert Space p. 52 Scalar product p. 52 Closest point in a closed convex subset p. 54 Linear functionals p. 56 Linear span p. 58 Applications of Hilbert Space Results p. 63 Radon-Nikodym theorem p. 63 Dirichlet's problem p. 65 Duals of Normed Linear Spaces p. 72 Bounded linear functionals p. 72 Extension of bounded linear functionals p. 74 Reflexive spaces p. 78 Support function of a set p. 83 Applications of Duality p. 87 Completeness of weighted powers p. 87 The Muntz approximation theorem p. 88 Runge's theorem p. 91 Dual variational problems in function theory p. 91 Existence of Green's function p. 94 Weak* Convergence p. 99 Uniform boundedness of weakly convergent sequences p. 101 Weak sequential compactness p. 104 Weak convergence p. 105 Applications of Weak Convergence p. 108 Approximation of the [delta] function by continuous functions p. 108 Divergence of Fourier series p. 109 Approximate quadrature p. 110 Weak and strong analyticity of vector-valued functions p. 111 Existence of solutions of partial differential equations p. 112 The representation of analytic functions with positive real part p. 115 The Weak and Weak* Topologies p. 118 Locally Convex Topologies and the Krein-Milman Theorem p. 122 Separation of points by linear functionals p. 123 The Krein-Milman theorem p. 124 The Stone-Weierstrass theorem p. 126 Choquet's theorem p. 128 Examples of Convex Sets and Their Extreme Points p. 133 Positive functionals p. 133 Convex functions p. 135 Completely monotone functions p. 137 Theorems of Caratheodory and Bochner p. 141 A theorem of Krein p. 147 Positive harmonic functions p. 148 The Hamburger moment problem p. 150 G. Birkhoff's conjecture p. 151 De Finetti's theorem p. 156 Measure-preserving mappings p. 157 Historical note p. 159 Bounded Linear Maps p. 160 Boundedness and continuity p. 160 Strong and weak topologies p. 165 Principle of uniform boundedness p. 166 Composition of bounded maps p. 167 The open mapping principle p. 168 Historical note p. 172 Examples of Bounded Linear Maps p. 173 Boundedness of integral operators p. 173 The convexity theorem of Marcel Riesz p. 177 Examples of bounded integral operators p. 180 Solution operators for hyperbolic equations p. 186 Solution operator for the heat equation p. 188 Singular integral operators, pseudodifferential operators and Fourier integral operators p. 190 Banach Algebras and their Elementary Spectral Theory p. 192 Normed algebras p. 192 Functional calculus p. 197 Gelfand's Theory of Commutative Banach Algebras p. 202 Applications of Gelfand's Theory of Commutative Banach Algebras p. 210 The algebra C(S) p. 210 Gelfand compactification p. 210 Absolutely convergent Fourier series p. 212 Analytic functions in the closed unit disk p. 213 Analytic functions in the open unit disk p. 214 Wiener's Tauberian theorem p. 215 Commutative B-algebras p. 221 Historical note p. 224 Examples of Operators and Their Spectra p. 226 Invertible maps p. 226 Shifts p. 229 Volterra integral operators p. 230 The Fourier transform p. 231 Compact Maps p. 233 Basic properties of compact maps p. 233 The spectral theory of compact maps p. 238 Historical note p. 244 Examples of Compact Operators p. 245 Compactness criteria p. 245 Integral operators p. 246 The inverse of elliptic partial differential operators p. 249 Operators defined by parabolic equations p. 250 Almost orthogonal bases p. 251 Positive compact operators p. 253 The spectrum of compact positive operators p. 253 Stochastic integral operators p. 256 Inverse of a second order elliptic operator p. 258 Fredholm's Theory of Integral Equations p. 260 The Fredholm determinant and the Fredholm resolvent p. 260 The multiplicative property of the Fredholm determinant p. 268 The Gelfand-Levitan-Marchenko equation and Dyson's formula p. 271 Invariant Subspaces p. 275 Invariant subspaces of compact maps p. 275 Nested invariant subspaces p. 277 Harmonic Analysis on a Halfline p. 284 The Phragmen-Lindelof principle for harmonic functions p. 284 An abstract Pragmen-Lindelof principle p. 285 Asymptotic expansion p. 297 Index Theory p. 300 The Noether index p. 301 Historical note p. 305 Toeplitz operators p. 305 Hankel operators p. 312 Compact Symmetric Operators in Hilbert Space p. 315 Examples of Compact Symmetric Operators p. 323 Convolution p. 323 The inverse of a differential operator p. 326 The inverse of partial differential operators p. 327 Trace Class and Trace Formula p. 329 Polar decomposition and singular values p. 329 Trace class, trace norm, and trace p. 330 The trace formula p. 334 The determinant p. 341 Examples and counterexamples of trace class operators p. 342 The Poisson summation formula p. 348 How to express the index of an operator as a difference of traces p. 349 The Hilbert-Schmidt class p. 352 Determinant and trace for operator in Banach spaces p. 353 Spectral Theory of Symmetric, Normal, and Unitary Operators p. 354 The spectrum of symmetric operators p. 356 Functional calculus for symmetric operators p. 358 Spectral resolution of symmetric operators p. 361 Absolutely continuous, singular, and point spectra p. 364 The spectral representation of symmetric operators p. 364 Spectral resolution of normal operators p. 370 Spectral resolution of unitary operators p. 372 Historical note p. 375 Spectral Theory of Self-Adjoint Operators p. 377 Spectral resolution p. 378 Spectral resolution using the Cayley transform p. 389 A functional calculus for self-adjoint operators p. 390 Examples of Self-Adjoint Operators p. 394 The extension of unbounded symmetric operators p. 394 Examples of the extension of symmetric operators; deficiency indices p. 397 The Friedrichs extension p. 402 The Rellich perturbation theorem p. 406 The moment problem p. 410 Historical note p. 414 Semigroups of Operators p. 416 Strongly continuous one-parameter semigroups p. 418 The generation of semigroups p. 424 The approximation of semigroups p. 427 Perturbation of semigroups p. 432 The spectral theory of semigroups p. 434 Groups of Unitary Operators p. 440 Stone's theorem p. 440 Ergodic theory p. 443 The Koopman group p. 445 The wave equation p. 447 Translation representation p. 448 The Heisenberg commutation relation p. 455 Historical note p. 459 Examples of Strongly Continuous Semigroups p. 461 Semigroups defined by parabolic equations p. 461 Semigroups defined by elliptic equations p. 462 Exponential decay of semigroups p. 465 The Lax-Phillips semigroup p. 470 The wave equation in the exterior of an obstacle p. 472 Scattering Theory p. 477 Perturbation theory p. 477 The wave operators p. 480 Existence of the wave operators p. 482 The invariance of wave operators p. 490 Potential scattering p. 490 The scattering operator p. 491012 The Lax-Phillips scattering theory p. 493 The zeros of the scattering matrix p. 499 The automorphic wave equation p. 500 A Theorem of Beurling p. 513 The Hardy space p. 513 Beurling's theorem p. 515 The Titchmarsh convolution theorem p. 523 Historical note p. 525 Texts p. 527 Riesz-Kakutani representation theorem p. 529 Positive linear functionals p. 529 Volume p. 532 L as a space of functions p. 535 Measurable sets and measure p. 538 The Lebesgue measure and integral p. 541 Theory of distributions p. 543 Definitions and examples p. 543 Operations on distributions p. 544 Local properties of distributions p. 547 Applications to partial differential equations p. 554 The Fourier transform p. 558 Applications of the Fourier transform p. 568 Fourier series p. 569 Zorn's Lemma p. 571 Author Index p. 573 Subject Index p. 577 Table of Contents provided by Syndetics. All Rights Reserved.
기본정보
ISBN | 9780471556046 ( 0471556041 ) |
---|---|
발행(출시)일자 | 2002년 04월 04일 |
쪽수 | 608쪽 |
크기 |
161 * 243
* 34
mm
/ 957 g
|
총권수 | 1권 |
언어 | 영어 |
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