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| Авторизация |
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| Moiseiwitsch B.L. — Integral Equations |
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| Предметный указатель |
 function 8 79
kernel 9
 space 74
 function 8
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,  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, 9
Kernel, 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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