Hagen R., Roch S., Silbermann B. — C-Algebras and Numerical Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Hagen R., Roch S., Silbermann B. — C-Algebras and Numerical Analysis

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Название: C-Algebras and Numerical Analysis

Авторы: Hagen R., Roch S., Silbermann B.

Аннотация:

To those who might think that using C*-algebras to study properties of approximation methods as unusual and even exotic, Hagen (mathematics, Freies Gymnasium Penig), Steffen Roch (Technical U. of Darmstadt), and Bernd Silbermann (mathematics, Technical U. Chemnitz) invite them to pay the money and read the book to discover the power of such techniques both for investigating very concrete discretization procedures and for establishing the theoretical foundation of numerical analysis. They speak both to students wanting to see applications of functional analysis and to learn numeral analysis, and to mathematicians and engineers interested in the theoretical aspects of numerical analysis.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 376

Добавлена в каталог: 09.04.2005

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Предметный указатель

$\varepsilon$ -invertibility      119
$\varepsilon$ -kernel      123
$\varepsilon$ -kernel of a non-negative op.      122
$\varepsilon$ -pseudospectrum      119
$\varepsilon$ -range      123
$\varepsilon$ -regularization      84
$\varepsilon$ -regularization of a matrix      79
$\varepsilon$ -regularization of a non-negative op.      123
$\varepsilon$ -stable sequence      127
Absolute value of an operator      340
Algebra      15 35
Algebra, antiliminal      223
Algebra, Banach algebra      36
Algebra, C*-algebra      53
Algebra, Calkin algebra      36 152
Algebra, Douglas algebra      170
Algebra, dual      227
Algebra, elementary      214
Algebra, Folner algebra      341
Algebra, Fredholm inverse closed      298
Algebra, irrational rotation algebra      352
Algebra, liminal      223
Algebra, normed      36
Algebra, postliminal      223
Algebra, primitive      216
Algebra, semi-simple      55
Algebra, simple      210
Algebra, singly generated      154
Algebra, standard      258
Algebra, Szego algebra      345
Algebra, Toeplitz algebra      56
Algebra, unital      35
Algebra, Wiener algebra      334
Algebras, product of      226
Algebras, restricted product of      226
Algebras, ultraproduct of      67
Annihilator      227
Approximation method      26
Approximation method, $\varepsilon$ -stable      127
Approximation method, applicable      26
Approximation method, collocation method      31 183
Approximation method, finite section method      31
Approximation method, Galerkin method      187
Approximation method, Moore — Penrose stable      87
Approximation method, projection method      28
Approximation method, spectrally stable      114
Approximation method, stable      26
Approximation method, stably regularizable      87
Arverson dichotomy      333
Bergman space      30
Center      149
CHARACTER      146
Circulant matrix      190
Circulant matrix, paired circulant      190
Collocation method      31 183
Collocation method, Bergman Toeplitz op.      52
Collocation method, singular integral op.      183
Composition series      225
Composition series, length of a      225
Condition number      63 79
Condition number, generalized      100
Convex hull      66
Convolution operator      230
Deficiency of a sequence      305
Deficiency of an operator (cokernel dimension)      36
Douglas algebra      170
Eigenvalue      12
Eigenvector      12
Element of an algebra of central rank one      283
Element of an algebra of finite central rank      283
Element of an algebra, centrally compact      283
Element of an algebra, invertible      35
Element of an algebra, Moore — Penrose invertible      89
Element of an algebra, normal      113
Element of an algebra, unit element      35
Families of homomorphisms      243
Families of homomorphisms, sufficient      243
Families of homomorphisms, weakly sufficient      244
Finite section method      31
Finite section method, band-dominated op.      200
Finite section method, singular int. op.      187 220
Finite section method, Toeplitz operator on       49 159
Finite section method, Toeplitz operator on Bergman space      52
Folner algebra      341
Fourier transform      230
Fractal *-homomorphism      67
Fractal algebra      67
Fractal approximation method      66
Fractal sequence      67
Function, almost periodic      232
Function, characteristic      167
Function, locally sectorial      348
Function, piece wise continuous      151
Function, quasicontinuous      170
Function, quasicontinuous, piecewise      175
Function, set function      106
Galerkin method      187
Gelfand transform      148
Generator of an algebra      154
Homeomorphism      149
Homomorphism      35
Homomorphism, *-homomorphism      54
Homomorphism, unital      35
Ideal      35
Ideal, *-ideal      54
Ideal, dual      227
Ideal, dual, largest      227
Ideal, liminal      223
Ideal, maximal      146
Ideal, maximal, maximal ideal space      147
Ideal, primitive      210
Ideal, projection lifting      94
Ideal, trivial      35
Idempotent      89
Index of a sequence      287
Index of an operator      36

Involution      53
Isomorphism      35
Laguerre polynomial      30 231
Least square solution      76
Lifting of an ideal      238
Lifting theorem      158
Limes inferior of a set seq.      106
Limes superior of a set seq.      106
Limiting set      106
Limiting set, partial      106
Limiting set, uniform set      106
Mean motion      233
Moore — Penrose-inverse      12 76
Moore — Penrose-invertibility      89
Moore — Penrose-invertible operator      80
Moore — Penrose-projection      90
Moore — Penrose-stable sequence      87
N ideals lemma      238
Nullity of a sequence      305
Nullity of an operator (kernel dimension)      36
Numerical range      134
Numerical range, algebraic      134
Numerical range, spatial      134
Operator of convolution      230
Operator of regular type      42
Operator polynomial      128
Operator, almost Mathieu operator      354
Operator, band      198 342
Operator, band dominated      198
Operator, bounded below      42
Operator, Fredholm operator      36
Operator, Fredholm operator of second kind      29
Operator, Hankel operator      45
Operator, Hilbert — Schmidt operator      30
Operator, Hille — Tamarkin operator      29
Operator, Laurent operator      45
Operator, limpotent      112
Operator, Moore — Penrose invertible      80
Operator, non-negative      84
Operator, normally solvable      42
Operator, nuclear      340
Operator, partial isometry      84 257
Operator, reflection      57
Operator, shift      33 174 231
Operator, singular integral op.      178
Operator, Toeplitz operator      33 45
Operator, Toeplitz operator on Bergman space      52
Operator, Toeplitz operator on the quarter plane      229
Operator, trace class      340
Operator, Wiener — Hopf operator      230
Orthogonal sum of Hilbert spaces      228
Partial isometry      84 257
Partition of the identity      83
Point, essential      324
Point, transient      324
Polar decomposition      84
Projection      89
Projection method      28
Projection, interpolation projection      30
Projection, interpolation projection of Lagrange type      183
Projection, Moore — Penrose projection      90
Projection, projection lifting ideal      94
Quadrature methods      189
Raileigh quotient      134
Regularization, $\varepsilon$ -regularization      84
Regularization, Tychonov regularization      79
Representation      208
Representation, faithful      208
Representation, irreducible      209
Representation, unitary equivalence      210
Separation property      241
Sequence, $\varepsilon$ -stable      127
Sequence, alpha-number      287
Sequence, deficiency      305
Sequence, Fredholm sequence      285
Sequence, Fredholm sequence, index of a      287
Sequence, Fredholm sequence, weakly      305
Sequence, Moore — Penrose stable      87
Sequence, nullity      305
Sequence, spectrally stable      114
Sequence, stable      26
Sequence, stably regularizable      87
Set function      106
Shift operator      33 174 231
Singular integral      178
Singular value      77 119
Singular value decomposition      77
Singular value, splitting property of      88 305
Space of splines      167
Space, invariant subspace      209
Space, maximal ideal space      147
Space, state space      134
Space, totally disconnected      113
Spectral theorem      83
Spectrum      35
Spectrum of an algebra      210
Spectrum, essential      324
Spline space      167
Splitting property      88 305
Splitting property, finite      305
State      134
State space      134
State, tracial      344
Subalgebra      35
Subalgebra, inverse closed      55
Symbol      61 244
Symbol mapping      61
Szego algebra      345
Toeplitz algebra      56
Topology, *-weak      148
Topology, discrete      227
Topology, hull-kernel      211
Topology, Jacobson      211
Topology, strong      13
Trace of an operator      336
Two projections theorem      181
Wiener algebra      334

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