Gohberg I., Goldberg S. — Basic Operator Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Gohberg I., Goldberg S. — Basic Operator Theory

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Название: Basic Operator Theory

Авторы: Gohberg I., Goldberg S.

Аннотация:

Basic Operator Theory provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, Basic Operator Theory begins with the geometry of Hilbert space and proceeds to the spectral theory for compact self-adjoint operators with a wide range of applications. Part of the volume is devoted to Banach spaces and operators acting on these spaces.

Presented as a natural continuation of linear algebra, Basic Operator Theory provides a firm foundation in operator theory, an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1981

Количество страниц: 285

Добавлена в каталог: 08.05.2008

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Предметный указатель

space      269
Absolutely continuous function      140
Adjoint operator      77
Almost periodic function      37
Analytic operator valued function      231
Baire category theorem      277
Banach space      194
Basic system of eigenvectors and eigenvalues      115
Basis, for a vector space      6
Basis, for a vector space, orthonormal      26
Basis, for a vector space, Schauder      201 242
Basis, for a vector space, standard for       22
Bessel’s inequality      25
Biorthogonal system      205
Bounded linear functionals, representation of      201-203
Bounded linear operator      52
Cauchy sequence      9
Cauchy — Schwartz inequality      2
Closed graph theorem      221 278
Closed operator      220
Closed set      19
Closure of a set      19
Codimension      243
Compact operator      83
Compact operator, characterization of      187
Compact operator, function of      160
Compact operator, normal, characterization of      183
Compact operator, self adjoint, characterization of      113
Compact operator, spectrum of      248
Compact set      261
Complement of a subspace      205 225
Complete inner product space      9
Complete normed linear space      194
Complete orthonormal system      28
Complex n-space      1
Conjugate of an operator      245
Conjugate space of       201
Conjugate space of       202
Continuity of an operator      57
Contraction      256
Contraction mapping theorem      256
Convergence of a sequence      8
Convex set      19
Countable set      265
Diagonalization, simultaneous      181
Differential equation      257
Differential equation in Hilbert space      165
Differential operators      140—147
Dimension of a vector space      6
Dini’s theorem      135
Direct sum      205
Distance from a point to a subspace      10
Distance from a point to a subspace, formula for      14
Eigenvalues, eigenvectors      106
Eigenvalues, eigenvectors of operators of finite rank      108
Eigenvalues, eigenvectors, basic system of      115
Eigenvalues, eigenvectors, simple      145
Equivalent norms      197 222
Essentially bounded function      270
Finite dimensional space, characterization of      198 199
Finite rank operator      63
Finite rank operator, approximation by      241
Finite rank operator, decomposition of      240
Fixed point      255
Fourier coefficient      26 30
Fourier series      30
Fredholm alternative      245
Function of a compact self adjoint operator      160
Gram determinant      13
Gram — Schmidt orthogonalization procedure      21
Graph of an operator      220
Green’s function      140 143
Hadamard’s inequality      15
Hahn — Banach theorem      203 276
Harmonic oscillation, simple      155
Hilbert Schmidt theorem      132
Hilbert space      9
Holder’s Inequality      271
Image of an operator      63
Imaginary part of an operator      182
Implicit function theorem      259
Incompatible systems of equation      16

Infective      65
Inner product      7
Inner product space      7
Integra-differential equation      168
Integral equation of the second kind      74 179
Integral operator      56 212
Integral operator, adjoint of      77
Interior point      277
Invariant subspace      88
Inverse of an operator      65 70
Inverse of an operator, approximation of      215
Invertible operator      65
Invertible operator of finite rank      66
Isometry      184
Iterative methods      174
Kernel function      56
Kernel of an operator      65
Kronecker delta      32
Lebesgue dominated convergence theorem      269
Lebesgue dominated convergence theorem, integrability      268
Lebesgue dominated convergence theorem, measure zero      267
Matrix representation of an operator      59 211
Mercer’s theorem      136
Metric space      261
Min.-max. theorem      122
Multiplicity of an eigenvalue      117
Non-negative operator      121
Norm      7 194
Norm of an operator      52
Normal operator      183
Normed linear space      194
Normed linear space, complete      194
One-one operator      65
Orthogonal complement      21
Orthogonal projection      82
Orthogonal vectors      10
Orthonormal basis      26
Orthonormal basis, examples of      27
Orthonormal basis, stability of      33
Orthonormal system      10
Oscillating string, displacement of      155
Parallelogram law      8
Parseval’s equality      27
Partially ordered set      273
Positive operator      121
Projection      225
Projection of a vector      35
Pythagorean Theorem      10
Range of an operator      63
Rank of an operator      63
Real part of an operator      182
Regular point      226
Resolvent      231
Resolvent set      226
Riesz representation theorem      61
Schauder basis      201 242
Schwarz inequality      8
Self adjoint operator      81
Self adjoint operator, compact      113
Self adjoint operator, normal      183
Separable Hilbert space      34 265
Separable Hilbert space, normed linear space      200
Shift operator, left, right      56
Span of a set      6
Spectral theorem for compact normal operator      183
Spectral theorem, for compact self adjoint operator      113 118
Spectrum of an operator      226
Sturm — Liouville system      142
subspace      6
Subspace, invariant      88
Surjective      70
Toeplitz matrix      60
Totally ordered set      273
Triangle inequality      8
Uniform boundedness principle      223
Unitary operator      185
Vector space      6
Volterra integral operator      230
Weierstrass approximation theorem      28
Weierstrass approximation theorem, second approximation theorem      29
with external force      157
wronskian      143
Zorn’s Lemma      273

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