Hagen R., Roch S., Silbermann B. — Spectral Theory of Approximation Methods for Convolution Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Hagen R., Roch S., Silbermann B. — Spectral Theory of Approximation Methods for Convolution Equations

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Название: Spectral Theory of Approximation Methods for Convolution Equations

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

Аннотация:

The aim of this book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, are covered and studied. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras, as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 373

Добавлена в каталог: 02.03.2006

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Предметный указатель

Algebra, Banach      1
Algebra, C*      3
Algebra, Calkin      4 147
Algebra, semi-simple      3
Algebraization      24
Applicability of an approximation method      7 244
Approximation method, cutting off the infinity      270
Approximation method, double indicated      227
Approximation method, multiindiced      242
Canonical projection      86
Carleman shift      344
Center      14
Central subalgebra      14
Collocation method for equations on R      211 213
Collocation method on complicated curves      328
Collocation method, non-equidistant partitions      350
Collocation method, numerical examples      329
Collocation projection      103
Commutator property      87
Compatible pair of arcs      282
Composed curve      282
Compression of F      92
Convergence, strong      4
Convergence, uniform      4
Convergence, weak      4
Costabel's decomposition      50
Cut-off-method      227 242
Cutting off singularities      325 340
de Boor-type estimate      80
Essentialization      25
Finite section method      228
Finite section method for block Toeplitz operators      235
Finite section method for operators with Carleman shift      347
Finite section method for operators with flip      345
Finite section method for paired operators      229
Finite section method for singular integral operators      337
Finite section method for Toeplitz + Hankel operators      348
Finite section method for Toeplitz operators      19
Finite section method, cutting off singularities      340
Fourier transform      46
Galerkin method      225 260 321
Galerkin method for equations on $R^{+}$       58 114
Galerkin method for equations on R      56 108 206
Galerkin method for equations on [0,1]      58 209
Galerkin method for Mellin convolutions      59 115
Galerkin method, cutting off singularities      268
Galerkin method, modified      255 258 260 265 275
Galerkin projection      54 102 291 295 301
Gelfand transform      13
Homomorphism      2
Ideal      3
Identification      26
Index of an operator      6
Infinite section method      237
Inverse closedness      2 29
Invertibility, approximate      11
Invertibility, essential      11
Invertibility, essential approximate      11
Invertibility, usual      11
KMS-algebra      32
Kozak's identity      237
Lifting theorem      25
Local inclusion theorem      34
Local principle, Allan's      14
Local principle, Douglas'      17
localization      26
Locally equivalent representations      27

Maximal ideal      3
Maximal ideal space      13
Mellin transform      47
Method of discrete whirls      119
Mother wavelet      100
Multiplier, $l^{p}(\alpha)$       59
Multiplier, continuous      60
Multiplier, piecewise continuous      60
Multiresolution analysis      100
Normally solvable      6
Operator of local type      197
Operator of regular type      6
Operator, conjugation      335 352
Operator, discrete flip      76 269 344
Operator, discretized Mellin convolution      64
Operator, double layer potential      352 354
Operator, flip      52 267
Operator, Fourier convolution      46
Operator, Fredholm      6
Operator, generalized Hankel      49
Operator, Hankel      18
Operator, homogeneous      62
Operator, Mellin convolution      48
Operator, projection      7
Operator, singular integral      46 283 289
Operator, Toeplitz      18
Operator, weighted generalized Hankel      49
Operator, weighted singular integral      49
Partition, non-equidistant      350
Partition, non-uniform      350
Partition, uniform      350
Piecewise constant      54 90
Piecewise continuous function      146 281
Piecewise polynomial with defect      97
Pilidi's method      312 34
Point, regular      282
Point, singular      282
Prebasis      91
Premeasure      85
Prespline      79
Prespline, canonical      82
Quadrature method for double layer potential operators      354
Quadrature method for equations on R      118 120 215
Quadrature method for Mellin convolutions      121 122
Quadrature method for singular integral operators      215
Quadrocation method      123
Quadrocation method for singular integral operators      217
Qualocation method for equations on R      214
Qualocation projection      104
Radical      3
Sequence of local type      199
Sequence, generalized      242
Sequence, infinite-section      227
Simple are      281
Singularity, analytic      225 226
Singularity, geometric      225 226
Singularity, numeric      226
Smoothest piecewise polynomial      97
Spectrum      2
SPLINE      79
Spline projection, cutting-off singularities      245
Spline space      54 79 294 300
Stability of a generalized sequence      244
Stability of an operator sequence      7
Symbol mapping      2
Wavelet      100
Winding number      78

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