Demidov A.S. — Generalized Functions in Mathematical Physics: Main Ideas and Concepts :: Электронная библиотека попечительского совета мехмата МГУ

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Demidov A.S. — Generalized Functions in Mathematical Physics: Main Ideas and Concepts

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Название: Generalized Functions in Mathematical Physics: Main Ideas and Concepts

Автор: Demidov A.S.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 131

Добавлена в каталог: 25.06.2008

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Предметный указатель

$\delta$ -function      5
$\delta$ -sequence      5
Bundle, cotangent      108
Cauchy — Riemann equations      11
Characteristic      49 52
Cokernel of an operator      105
Compact      6
Condition of complementability      110
Condition, boundary      11 48
Condition, Hugoniot      53
Condition, initial      48
Condition, Shapiro — Lopatinsky      110
Convergence      33
Convolution      14 92 93
Cover, locally finite      9
Degree of a mapping      102
Dirac function      5
Dirichlet problem      11
Distance      33
distribution      70
Eigenfunction      77
Eigenvalue      77
Ellipticity with a parameter      114
Equality, Parseval      83
Equation, Burgers      52
Equation, Laplace      11
Equation, Poisson      11
Equation, string      50
Equation, wave      50
Equations, Cauchy — Riemann      11
Estimate, a priori      98
Extension of the functional      61
Factorization      109
Formula, Gauss, integral      26
Formula, Green      27
Formula, Green, first      26
Formula, Green, second      26
Formula, Newton — Leibniz      25
Formula, Ostrogradsky — Gauss      25
Formula, Poincare      25
Formula, Poisson      13
Fourier, transform, inverse      82
Function, analytic of one complex variable      11
Function, Dirac      5
Function, generalized      59 120
Function, Green      27
Function, harmonic      11
Function, Heaviside      42
Function, Lebesgue integrable      31
Function, measurable      30
Function, smoothing      37
Function, step      30
Function, tempered      84
Index of an operator      106
Index of factorization      109
Inequality, Hoelder      36
Inequality, Minkowski      36
Inequality, Peetre      100
Integral, Lebesgue      31
Integral, Poisson      13
Kernel of an operator      105
kernel, Poisson      14
Ladder, Cantor      58
Laplacian      11
Lemma on change of variables      101
Lemma on composition      100
Lemma on continuity      99
Lemma, Fatou      32
Lemma, Giraud — Hopf — Oleinik      18
Lemma, L. Schwartz      107
Measure      31
Method, Fourier      78
Method, Fourier, of separation of variables      78
Norm      32
Number, complex, generalized      120
Operator, compact      108
Operator, continuation      106
Operator, elliptic      100 108 111
Operator, Laplace      11
Operator, pseudodifferential      98
Operator, pseudodifferential of class L      101
Operator, pseudodifferential with a symbol a      109
Operator, restriction      96
Operator, smoothing      100
Operator, totally continuous      108
Partition of unity subordinate to a locally finite cover      9
Poisson integral      13
Principle, maximum      15
Principle, maximum, strong      17

Principle, minimum      16
Principle, superposition      14
Problem of regularization      61
Problem with the directional derivative      102
Problem with the skew derivative      102
Problem, Dirichlet      11
Problem, elliptic      111
Problem, Hilbert      104
Problem, mixed      48
Problem, Neuman      102
Problem, Poincare      111
Product, scalar      76
Regulizer      108
Sequence, fundamental      33
Sequence, weakly converging      59
Series, Fourier      75
Series, Fourier, in an orthogonal system of functions      79
Set of zero measure      30
Set, annihilating, of a functional      61
Set, Cantor      33
Set, compact      6
Set, compactly embedded      7
Set, measurable      31
Solution, fundamental      57 91
Space, $C^{m}(\Omega)$ of functions m-times continuously differentiable up to the boundary      6
Space, $C^{\infty}(\Omega)$ , ..., $C_{0}^{\infty}(\Omega)$ of infinitely differentiable functions      7
Space, $C_{0}^{m}(\Omega)$ of functions with compact support in $\Omega$       6
Space, $C_{0}^{m}(\overline{\Omega})$ of functions with compact support in $\overline{\Omega}$       6
Space, $C_{b}^{m}(\Omega)$ of m-times continuously differentiable functions with bounded derivatives      6
Space, $L^{p}(\Omega)$ functions integrable in pth power      35
Space, $L^{\infty}(\Omega)$ of essentially bounded functions      39
Space, $L_{loc}^{\infty}(\Omega)$ of functions locally integrable in pth power      40
Space, $PC^{m}(\Omega)$ of functions m-times piece-wise continuously differentiable      6
Space, $PC_{b}^{m}(\Omega)$ of functions m-times piece-wise continuously differentiable and bounded      6
Space, $\mathcal{D}'(\Omega)$ of distributions      70
Space, $\mathcal{D}(\Omega)$ of test functions      69
Space, $\mathcal{D}^{#}(\Omega)$ of generalized functions      59
Space, $\mathcal{D}^{b}(\Omega)$ of Sobolev derivatives      56
Space, $\mathcal{E}'(\Omega)$ of distributions with a compact support      70
Space, $\mathcal{E}(\Omega)$ of infinitely differentiable test functions      70
Space, $\mathcal{G}(\Omega)$ of generalized functions      120
Space, $\mathcal{S}'(\mathbb{R}^{n})$ of tempered distributions      84
Space, $\mathcal{S}(\mathbb{R}^{n})$ of rapidly decreasing functions      82
Space, Banach      33
Space, dual      39
Space, Hilbert      76
Space, metric      33
Space, metric, complete      33
Space, Prechet      73
Space, Sobolev      94
Space, Sobolev $W^{p,k}(\Omega)$       80
Space, topological      72
Space, topological, linear locally convex      72
Superposition      14
Support      6 61
Symbol      98
Symbol of an operator      101
Symbol, principal      109
System, acoustic      42
System, complete in a Banach space      79
Theorem on compactness of the embedding      97
Theorem on discontinuous majorant      16
Theorem on partition of unity      9
Theorem on stability of the index      113
Theorem on the general form of distributions      71
Theorem on the mean value      17
Theorem, Banach      107
Theorem, Beppo Levi      32
Theorem, E. Borel      64
Theorem, F. Riesz      39
Theorem, Fischer and F. Riesz      32
Theorem, Fubini      34
Theorem, L. Schwartz      70
Theorem, Lebesgue      32
Theorem, Paley — Wiener      90
Theorem, Sobolev embedding      94
Theorem, Sobolev on traces      95
Theorem, Weierstrass      93
Trace      95
Transform, Fourier      80
Transform, Fourier — Laplace      90
Transform, Fourier, in the complex domain      90
Transform, Fourier, inverse of the distribution      84
Transform, Fourier, of the distribution      84
Transformation, Fourier      80
Transformation, Laplace      89
Value principal      57
Variables, separated      77
Vector, cotangent      108
Wave, shock      52

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