Estrada R., Kanwal R.P. — A distributional approach to asymptotics theory and applications :: Электронная библиотека попечительского совета мехмата МГУ

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Estrada R., Kanwal R.P. — A distributional approach to asymptotics theory and applications

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Название: A distributional approach to asymptotics theory and applications

Авторы: Estrada R., Kanwal R.P.

Аннотация:

This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2002

Количество страниц: 453

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\delta$ -derivatives      80
$\mathcal{D}'(U)$       56
$\mathcal{D}(U)$       55
$\mathcal{E}'(U)$       70
$\mathcal{E}(U)$       71
$\mathcal{E}\{\phi_{n}\}$       92
$\mathcal{E}^{'}\{\phi_{n}\}$       92
$\mathcal{G}_{\beta}$       335
$\mathcal{H}'(\Omega)$       132
$\mathcal{H}(\Omega)$       132
$\mathcal{K}$       88
$\mathcal{K}'$       89
$\mathcal{O}_{C}$       88
$\mathcal{O}_{C}'$       88
$\mathcal{O}_{exp}$       84
$\mathcal{O}_{M}$       88
$\mathcal{O}_{q}$       88
$\mathcal{P}$       87
$\mathcal{P}'$       88
$\mathcal{S}$       82
$\mathcal{S}'$       82
$\pi$ -topology      222
$\sigma$ -topology      222
$\varepsilon$ -topology      222
Abel partial summation      33 49
Abel summability      266 299
Abel summability of distributional evaluations      300
Abel summability, principal value      299
Airy functions      140
Algebraic singularity      63
Analytic representation      400
Arithmetical function      34
Associated homogeneous function      72
Associated vectors      75
Asymptotic development      8
Asymptotic equivalence      4
Asymptotic evaluation of indefinite integrals      26
Asymptotic evaluation of sums      26
Asymptotic expansion      8
Asymptotic expansion of analytic functions      21
Asymptotic expansion, extended      12
Asymptotic expansion, multiplicative      44
Asymptotic expansion, strong      18
Asymptotic power series      21
Asymptotic power series, differentiation      23
Asymptotic power series, existence      25
Asymptotic sequence      8
Asymptotic sequence, associated spaces      90
Asymptotically homogeneous function      362
Bernoulli numbers      37
Bernoulli polynomials      36
Bessel equation      431
Bessel function      86
Bessel function of imaginary argument      175
Bessel function of the third kind      178
Bessel function, modified      175
Bessel polynomials      405 406
Big O      3
Big O, $O_{+}$       7
Big O, $O_{-}$       1
Biorthogonal sequences      398
Borel theorem      20
Boundary layer      410
Boundary layer function      417
Cauchy representation      400
Cauchy’s formula      44
Caustic      213
Cesaro limit      308
Cesaro limit of spherical means      324
Cesaro summability      266 301 302
Cesaro summability of distributional evaluations      309
Cesaro summability, principal value      354
Cesaro — Riesz behavior      305
Cesaro — Riesz means      304
Chapman’s formula      150
CHARACTER      254
Characteristic value      75
Characteristic vector      75
Coincidence limit      386
col      135
Complete contraction      55
Contour line      135
Convolution      86
Convolutor      88
Corner      201
Counting function      316
Critical point      145 205
CYCLE      176
Cylinder function      384
Cylinder kernel      383
Degenerate distributional kernel      233
Deleted neighborhood      2
Digamma function      100 124
Dilatation operator      75
Dipole layer      80
Dirac delta function      53 56 132
Dirichlet kernel      356
Dirichlet L-function      254
Dirichlet multiplication      272
dispersion relation      212
Dispersive wave propagation      212
distribution      55
Distribution of rapid decay      87
Distribution of slow growth      82
Distribution, differentiation      60
Distribution, linear changes of variables      59
Distribution, multiplication      61
Distribution, non-linear change of variables      62
Distribution, order      72
Distribution, periodic      89 196
Distribution, regular      56
Distribution, regularizable      326
Distribution, restriction      70
Distribution, singular      56
Distribution, tempered      82
Distribution, translation      59
Distribution, value at a point      169
Distributional convergence      57
Distributional lateral value      170
Distributional limit at a point      170
Distributionally small function      118 192
Distributionally small sequence      264
Dual sequences      398
Dual Taylor series      399
Duality      59
Epstein zeta function      349
Error function      44
Euler constant      31
Euler numbers      390
Euler — Maclaurin formula      36 37
Exponential integral function      10
Fejer kernel      357
Formal power series      285
Fourier kernel      225
Fourier series of Bernoulli polynomials      39
Fourier transform      82 226
Fourier transform, finite      148 210
Fourier transform, restriction theorems      211
Fourier type integrals      205
Fresnel integrals      44
Functional approach      54
Fundamental form      80
Gamma function      48 100
Gauge function      4 161
Gaussian curvature      210
Generating function      41 284
Green function      317
Green kernel      379
Group velocity      213
Hadamard finite part      67 92

Hankel function      178
Hankel’s integral      177
Hansen’s expansion      175
Heat equation      428
Heat kernel      381
Heaviside function      60
Heisenberg distributions      67
Hermite polynomials      406
Hoelder summability      301
Homogeneous function      72 93
Hurwitz zeta function      48 254 348
Hyperasymptotic expansion      131
Hyperfunction      398
Inner expansion      428
Inner part      414
Inner-outer decomposition      414
Integral part      12
Integrated trace      317
Jump discontinuity      76
Kelvin’s formula      146
Klein — Gordon equation      212
Komatsu’s theorem      407
Kronecker delta      402
Lagrange’s inversion formula      112 172
Lambert series      255
Landau symbols      see "Order symbols"
Laplace’s formula      127 198 202 236
Layers      57
Legendre polynomials      174
Level curve      135
Level of accuracy      11
Limit superior      3
Little o      3
Littlewood’s Tauberian theorem      299 391
Locally integrable      56
Logarithmic scales      8
L’Hopital’s Rule      6 10 43
Macdonald function      173
Mellin transform      340
Method of steepest descent      133
Metric space      19
Moment asymptotic expansion      113 118 121 234
Moment asymptotic expansion, generalized      118
Moment asymptotic expansion, generalized partial      224
Moment asymptotic expansion, multidimensional      191
Moment asymptotic expansion, partial      224
Moment function      340
Moments      89 113 191
Moments, generalized      154 159
Moments, partial      225
Moments, problem of      399
Moyal algebra      88
Much smaller      5
Multilayer      80
Multiplier      233
Noncommutative residue      388
Order symbols      2
Order symbols, $O_{+}$       7
Order symbols, $O_{-}$       7
Order symbols, $\Omega$       7
Order symbols, $\Omega_{+}$       8
Order symbols, $\Omega_{-}$       8
Order symbols, $\thicksim$       4
Order symbols, O      3
Order symbols, one sided      7
Orthogonal polynomials      405
Oscillatory integral      145
Outer expansion      428
Outer part      414
Parabolic cylinder function      174
Parseval relation      82
Partition      281
Partition, unrestricted      284
Pentagonal numbers      286
Periodic sequence      254
Planck’s constant      228
Plane wave      213
Pointed neighborhood      2
Poisson bracket      228
Poisson kernel      354
Power series      1
Principal value      56 64 159
Principle of Stationary Phase      145
Problem of moments      399
Pseudodifferential operator      369
Pseudofunction      68
Pseudolocal operator      370
Quasiasymptote      161
Quasiasymptotic expansion      170
Quasiasymptotic expansion of the first kind      171
Quasiasymptotic expansion of the second kind      171
Radon measure      72
Ray      213
Regularization      63 91 325
Regularization, analytic continuation      64
Regularization, canonical      69 170
Regularization, Hadamard finite part      67 92
Regularization, principal value      64
Regularly varying function      162
Regularly varying function at the origin      169
Relief surface      135
Remainder term      1
Riemann zeta function      32 310
Riemann — Lebesgue lemma      181
Riesz typical means      267 304
Ritt's theorem      19
Saddle point      135
Saddle point approximation      138
Schmidt topology      222
Schroedinger equation      428
Schroedinger kernel      381
Secant coefficients      390
Sharpe’s equation      431
Sifting property      54
Sine integral function      12
Singular frequencies      212
Singular perturbations      408 411
Singular support      72
Slowly varying function      162
Smoothing operator      370
Spectral asymptotics      368
Spectral content asymptotics      422
Spectral decomposition      368
Spectral density      368
Spectral function      368
Spectral zeta function      352
Spherical-mean function      323
Square numbers      286
Steepest path      136
Stieltjes integral      155
Stieltjes integral, generalized      156 241
Stieltjes series      18
Stirling’s formula      5 43 47 48 50 123 129
Stokes’ lines      22 140
Stokes’ phenomenon      22
Strong developments      18
Summation convention      55
Support      70
Symbol      369
Symmetric functions      282
Symmetric product      79
Symplectic form      228
Tauberian theorem      299
Tauber’s theorem      391
Taylor approximation      9
Taylor expansion      108 188
Taylor polynomial      2 115 192
Taylor series      1 231
Taylor series, dual      399
Telescopic sum      28

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