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Moiseiwitsch B.L. — Integral Equations
Moiseiwitsch B.L. — Integral Equations

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Название: Integral Equations

Автор: Moiseiwitsch B.L.

Аннотация:

Geared toward upper-level undergraduate students, this text begins with a straightforward account, accompanied by simple examples of a variety of integral equations and the methods of their solution. The treatment becomes gradually more abstract, with discussions of Hilbert space and linear operators, the resolvent, Fredholm theory, and more. 1977 edition.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 173

Добавлена в каталог: 23.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^{2}$ function      8 79
$L^{2}$ kernel      9
$l_{2}$ space      74
$R^{2}$ function      8
$R^{2}$ kernel      9
Abel's integral equation      1 3 37
Abelian group      80
Abstract Hilbert space      80 109
Adjoint equation      99 110
Adjoint operator      89 99 110
Adjugate matrix      116
Associative law      80 86
Basis      70 73 83
bernoulli      14
Bessel function      37
Bessel's inequality      77 83
Best mean square approximation      77
Bifurcation point      11
Bilinear formula      139
Biorthogonal series      111
Bocher's example      109
Bounded linear operator      89
Bounds on characteristic values      146
Cauchy inequality      71
Cauchy principal value      56 63
Cauchy sequence      73 79 82
Cauchy — Riemann equations      57 63
Cauchy-type integral      56
Characteristic functions      101
Characteristic values      7 21 101 110 136
Characteristic values, bounds on      146
Characteristic vectors      110
Commutative law      80 86
Compact operator      92
Complete linear vector space      80
Complete orthonormal system      82
Complete space      74 76 79 82
Complete system      76 83
Completely continuous operators      92 111 125
Completeness relation      78 83
Continuous functions and kernels      44 102 126
Convergence of Neumann series      2 44
Convergence, strong      72 78 82
Convergence, weak      92
Convolution theorem for Fourier transform      25
Convolution theorem for Laplace transform      24
Convolution theorem for Mellin transform      25
Cramer's rule      116
Critical speeds      21
Degenerate kernels      7 114
Degenerate kernels, approximation by      120
Delta function      18
Dense      82
Difference kernel      5
Differential equations, first order      14
Differential equations, linear      14
Differential equations, second order      15 17
Dimension of Hilbert space      82
Dini's theorem      150
Dirac      18
Dirichlet's problem      2 55
Dissection      122
Distance      72
Distance function      81
Distributive law      80 86
Domain      89
du Bois-Reymond      1
Euclidean space, 3-dimensional      69
Euclidean space, n-dimensional      70
Expansion theorems      139
Expansion theorems for iterated kernels      143
Field      80
Finite Hilbert transform      65 67
Finite rank      114
Flexible string      16 153
Foeppl's integral equation      67
Fourier coefficients      77 91
Fourier transforms      1 25 26 29 35 40
Fox's integral equation      39
Fredholm alternatives      124
Fredholm determinant      129
Fredholm equations      2
Fredholm equations of first kind      3 34
Fredholm equations of second kind      3 26 43 98 102 109 144
Fredholm formulae      126
Fredholm minor      130
Fredholm theorems      121 124 125
Full orthonormal system      139
Function space      74 79
Function space, $L_{2}$      79
Fundamental set      82
Gamma function      38
Generalized functions      19
Gram — Schmidt orthogonalization      76 82
Green's function      18 54
Green's function in three dimensions      55
Green's function in two dimensions      54
Hadamard's inequality      130
Hermitian adjoint      88
Hermitian kernels      5 88 136 147
Higher dimensions      53
Hilbert formula      143
Hilbert integral operator      64
Hilbert kernel      61
Hilbert kernel, non-negative definite      147
Hilbert kernel, positive      147
Hilbert singular integral equation      65
Hilbert space      69 79
Hilbert space of sequences      71
Hilbert space, dimension of      82
Hilbert transform      63 64
Hilbert — Schmidt kernel      136
Hilbert — Schmidt series      141
Hilbert — Schmidt theorem      141
Homogeneous equation      3
Huygens tautochrone problem      2
Impulse function      19
INDEX      10 116
Influence function      20
Inner product      69 71 74 80
Integral equation, Abel's      1 3 37
Integral equation, convolution type      24
Integral equation, Foeppl's      67
Integral equation, Fox's      39
Integral equation, Fredholm, first kind      3 34
Integral equation, Fredholm, second kind      3 26 43 98 102 109 144
Integral equation, homogeneous      3
Integral equation, Lalesco — Picard      28
Integral equation, singular      9 53
Integral equation, Stieltjes      34
Integral equation, Volterra, first kind      3 4 36
Integral equation, Volterra, second kind      4 31 45 105
Integral operators      85
Integral operators, completely continuous      92
Integral operators, continuous      90 92
Integral operators, norm of      87
Integral transform      24
Integral transform, Fourier      1 25 26 29 35 40
Integral transform, Hilbert      63 64
Integral transform, Laplace      1 24 31 34 36 38
Integral transform, Mellin      25 39 40
Inverse element      80
Inverse point      59
Iterated kernels      46 143
Kernel      3
Kernel, $L^{2}$      9
Kernel, $R^{2}$      9
kernel, continuous      102
Kernel, convolution type      5
Kernel, degenerate      7 114 120
Kernel, difference      5 24
kernel, hermitian      5 88 136 147
Kernel, Hilbert      61
Kernel, Hilbert — Schmidt      136
Kernel, iterated      46 143
Kernel, matrix      91
Kernel, Pincherle — Goursat      114
Kernel, polar kernel      53
Kernel, positive      147
Kernel, regular value of      99 110
kernel, resolvent      6 47 145
Kernel, self-adjoint      88
Kernel, separable      6
Kernel, singular      4 9 53
Kernel, skew symmetric      119 154
Kernel, skew-hermitian      154
Kernel, square integrable      8
kernel, symmetric      4
Kernel, Weyl      11
Kneser      137
Lalesco — Picard equations      28
Laplace equation      2 55
Laplace transform      1 24 31 34 36 38
Lebesgue      8
Limit element      82
Linear integral equation      3
Linear manifold      89
Linear operators      85
Linear operators in Hilbert space      85
Linear operators, bounded      89
Linear operators, completely continuous      92
Linear operators, continuous      90 92
Linear operators, integral      85
Linear vector space      80
Liouville      2 43
Liouville — Neumann series      43
Matrix representation      91
Mean square, convergence      77
Mean square, limit      78
Mellin transform      25 39 40
Mercer's theorem      148
Metric      80
Minkowski's inequality      75
n-dimensional space      70
Neumann      2 43
Neumann series      43 102
Neumann series, convergence of      2 44 102
Non-linear equations      11
Norm      69 70 71 74 87 89
Normal operator      96
Null operator      87
Operator, adjoint      89 99 110
Operator, bounded      89
Operator, compact      92
Operator, completely continuous      92 111 125
Operator, continuous      90 92
Operator, hermitian      89
Operator, identity      86
Operator, integral      85
Operator, norm of      87
Operator, normal      96
Operator, null      87
Operator, resolvent      98 110
Operator, self-adjoint      89
Orthogonalization, Gram — Schmidt      76
Orthonormal system      70 75 82
Parseval's formula      78
Parseval's formula, generalized      78
Pincherle — Goursat kernel      114
poisson      2
Poisson's formula for half plane      60
Poisson's formula for unit disc      59
Polar kernel      53
Positive Hermitian kernel      147
RANGE      89
Rank      10 114 116
Rank, finite      10 114
Rank, infinite      10
Rayleigh — Ritz variational method      152
Regular value      99 110
Reimann      8
Resolvent equation      98 110
Resolvent kernel      6 47 145
Resolvent operator      98 110
Resolvent set      99
Riesz — Fischer theorem      79 140
Ritz      152
Scalar product      69
Schwartz's inequality      72 74 81
Self adjoint kernel      88
Shaft      21
Singular integral equations      9 53
Singular integral equations of Hilbert type      65
Singular kernels      4 9 53
Singular point      12
Space, complete      76 79 82
Space, Euclidean      69
Space, Hilbert      69 79
Spectrum      10 101 136
Square integrable functions      8
Square integrable kernels      8
Stieltjes integral equation      34
String      16 20 153
Strong convergence      72 78 82
Successive approximations, method of      2 43
Symmetric kernel      4
Tautochrone      2 37
Trace      133 144
Transforms, Fourier      1 25 26 29 35 40
Transforms, Hilbert      63 64
Transforms, Laplace      1 24 31 34 36 38
Transforms, Mellin      25 39 40
Trial function      153
Triangle inequality      70 72 75 81
Uniqueness theorem      99 105
Variational principles      150
Volterra      2
Volterra equation      2
Volterra equation of first kind      3 4 36
Volterra equation of second kind      4 31 45 105
Weak convergence      92
Weyl kernel      11
wronskian      20
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