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Duistermaat J.J, Kolk J.A.C. — Distributions: theory and applications
Duistermaat J.J, Kolk J.A.C. — Distributions: theory and applications

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Название: Distributions: theory and applications

Авторы: Duistermaat J.J, Kolk J.A.C.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: book draft

Год издания: 2006

Количество страниц: 300

Добавлена в каталог: 07.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{k}$ norm      32
$L^{2}$ inner product, $L^{2}$ norm      154
$\delta$-neighborhood      14
Absorbing sequence      60
Almost everywhere      31
Analytic continuation      124
Analytic function      15
Analytic singular support      116
Arzela — Ascoli theorem      5
Averaging with weight function      6
Backward cone      126
Banach space      103
Banach — Steinhaus theorem      44
Basis      62
Basis, dual      74 173
beta function      134
Binomial coefficients      19
Bolzano — Weierstrass theorem      13
Bounded linear mapping      63
Calculus of variations      3
Capacitor      80
Cauchy formula problem, uniqueness      131
Cauchy integral formula      115
Cauchy integral theorem      114
Cauchy problem, existence      192
Cauchy — Riemann operator      116
Chain rule      49
Characteristic function      21
Closure      2
Compact      11
Completeness      211
Completeness of $C_{0}^{\infty}$      44
Completion      211
complex derivative      113
Complex line integral      114
Complex-analytic      115
Complex-analytic family of distributions      124
Complex-analytic function, distribution-valued      124
Complex-analytic in several variables      116
Complex-differentiable      113
Complex-differentiable distribution      113
composition      50
Cone, backward      126
Cone, forward      126
Connected      15
Continuity of linear form      27
continuous      62
Continuous, Hoelder      206
Continuous, sequentially      62
Continuous, — inclusion      144
Continuous, — linear form      59
Continuous, — linear mapping      62
Convergence in $C^{\infty}(X)$      59
Convergence in $C^{\infty}_{0}(X)$      19
Convergence in $\mathcal{D'}(X)$      43
Convergence in $\mathcal{E'}(X)$      59
Convergence in $\mathcal{S'}(R^{n})$      150
Convergence in $\mathcal{S}(R^{n})$      144
Convergence of distributions      43
Convergence, weak      63
Convex      61 198
Convex, locally      61
Convolution      7
Covering, open      11
Cut-off function      21
Dense      60
Density of measure      34
Derivative in direction of outer normal      118
Derivative of distribution      39
Derivative, complex      113
Derivative, total      49
Determinant, Jacobi      79
Diffeomorphism      78
Differentiable family      81
Diffusion equation      45
Dipole vector      118
Dirac function      32
Dirac notation      32
Direct product      96
Dirichlet kernel      259
Dirichlet problem      119
Discrete      58
distribution      27
Distribution with compact support      64
Distribution, complex-differentiable      113
Distribution, derivative of      39
Distribution, extension of      54
Distribution, homogeneous      83
Distribution, multiperiodic      173
Distribution, order of      33
Distribution, periodic      87
Distribution, positive      34
Distribution, potential of      110
Distribution, reflected      80
Distribution, restriction of      53
Distribution, support of      54
Distribution, tempered      150
Distribution-valued complex-analytic function      124
Distributional extension      54
Distributional, sense, in      6
Distributional, solution of Cauchy problem      132
Distributions, convergence of      43
Divergence      1
Divergence theorem      2
Dual basis      74 173
Dual lattice      173
Dual, topological      28 63
Elliptic operator      180
Embedding      84
Equation, diffusion      45
Equation, Euler's differential      83
Equation, heat      45
Equation, Helmholtz'      120
Equation, Poisson's      110
Equations of Euler — Lagrange      4
Euler differential equation      83
Euler — Lagrange, equations of      4
Evaluation      32
Expectation      35
Extension of distribution      54
Family of distributions, complex-analytic      124
Family, differentiable      81
Fiber, integration over      86
Flow      82
Form, continuous linear      59
Form, linear      27
Form, monotone linear      35
Formula, Cauchy's integral      115
Formula, Fourier's inversion      149
Formula, Green's      119
Formula, Parseval's      149
Formula, Poisson's summation      171
Formula, Poisson's summation, in $R^{n}$      174
Formula, Pompeiu's integral      115
Formula, Radon's inversion      165
Formulas, Sokhotsky's      221
Forward cone      126
Fourier coefficient      167
Fourier integral operator      198
Fourier inversion formula      149
Fourier series in $\mathcal{S}'(R^{n})$      170
Fourier transform      142
Fourier — Laplace transform      144
Function, analytic      15
Function, Beta      134
Function, characteristic      21
Function, complex-analytic      115
Function, complex-analytic in several variables      116
Function, complex-differentiable      113
Function, cut-off      21
Function, Dirac      32
Function, distribution-valued complex-analytic      124
Function, Gamma      132
Function, harmonic      110
Function, Heaviside      40
Function, moment of      52
Function, rapidly decreasing      144
Function, real-analytic      116
Function, Riemann's "nondifferentiable"      46
Function, square-integrable      154
Function, support of      15
Function, test      15
Function, translated      7
Functional analysis      28
Functional, linear      27
Fundamental domain      173
Fundamental matrix      71
Fundamental solution      109
Gamma function      132
Gauss density      23
Green's formula      119
Group law      82
Hahn — Banach theorem      153
Harmonic      110
Heat equation      45
Heaviside function      40
Heine — Borel theorem      13
Helmholtz equation      120
Hilbert space      154
Hilbert transform      158
Hoelder continuous      206
Homogeneous distribution      83
Homotopy      134
Huygens principle      131
Hyperbolic operator      197
Hypoelliptic      111
In distributional sense      6
In weak sense      6
Inclusion, continuous      144
Increasing      60
Independent sum of probability measures      106
Inequality, Young's      106
Integer part      176
Integrable, locally      22 30
Integral kernel      112
Integral norm      103
Integral, complex line      114
Integral, Riemann — Liouville      126
Integration over fiber      86
Integration under distribution sign      93
Integration, Lebesgue      22
Integration, Riemann      22
Invariant, as density      83
Invariant, as generalized function      83
Inverse function theorem      78
Jacobi determinant      79
Jacobi, matrix      79
Jump relations      264
Kernel, Dirichlet      259
Klein — Gordon operator      199
Laplace operator      42
Laplace transform      144
Lattice      173
Lattice, dual      173
Layer      54
Layer, double      80
Layer, multiple      81
Lebesgue integration      22
Leibniz' formula      19
Leibniz' rule      19
Lemma, Weyl's      112
Lie group      175
Linear form      27
Linear form, continuous      59
Linear form, monotone      35
Linear functional      27
Linear mapping, bounded      63
Linear mapping, continuous      62
Linear partial differential operator      56
Liouville theorem      184
Locality property      215
Locality property, weak      215
Localization at infinity      215
Locally convex      61
Locally in $H_{(s)}$      203
Locally integrable      22 30
Lorentz group      127
Mapping, bounded linear      63
Mapping, continuous linear      62
Mapping, proper      77
Mapping, sum      96
Matrix, fundamental      71
Matrix, Jacobi      79
Mean of $u\in \mathcal{D}'(R^{n}/A)$      173
Mean, of distribution      168
Mean, of function      167
Measurable set      23
Measure      34
Measure, density of      34
Measure, Dirac      34
Measure, point      32
Measure, positive      35
Measure, probability      35
Measure, Radon      34
minimizing      4
Moderate growth      169
Moderate growth, multisequence of      173
Modulo $C^{\infty}$      111
Mollifier      8
Moment of function      52
Momentum operator      145
Monotone linear form      35
Multi-index      18
Multi-index, order of      18
Multiperiodic      173
Multisequence of moderate growth      173
Neighborhood      61
Norm, integral      103
Open covering      11
Operator commuting with translations      92
Operator, Cauchy — Riemann      116
Operator, elliptic      180
Operator, Fourier integral      198
Operator, hyperbolic      197
Operator, Klein — Gordon      199
Operator, Laplace      42
Operator, linear partial differential      56
Operator, momentum      145
Operator, position      70
Operator, pseudo-differential      182
Operator, singular integral      112
Operator, wave      113
Orbit      128
Order of distribution      33
Order of multi-index      18
Paley — Wiener theorem      190
Parametrix (distribution)      111
Parametrix, as operator      112
Parseval formula      149
Partition of unity      20
Periodic distribution      87
Plane wave      141
Point measure      32
Point source      2
Point, stationary      57
Poisson equation      110
Poisson summation formula      171
Poisson summation formula in $R^{n}$      174
Polynomial, Taylor      51
Pompeiu integral formula      115
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