|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Tricomi F.G. — Integral equations |
|
|
|
| Предметный указатель |
'Integrablo' 9
Abol equation 39
Adhemar, (d'), R. 231
Airfoil equation 173
Airy functions 34
Almost everywhere 10
Almost uniformly convergent 13 51
Alternative theorem 64
Approximation in the mean 84
Approximation in the mean, of a  -kernel 98
Associated eigenfunctions 61
Associated eigenfunctions, equation 61
Associated eigenfunctions, kernel 60
Asymptotic representation, of Bossel functions 37
Asymptotic representation, of eigenfunction s 135
Asymptotic representation, of eigenvalues 135
Asymptotic theorem (Hilbert transformation) 182
Bateman, H. 145
Bernoulli numbers 123
Bessel functions 32—38 159 229
Bessel functions, inequality 85
Betti-Maxwell principle 1 158
Bifurcation points 161 164 201
Biickner, H. 76 231
Bilinear formula 106 113
Bocher, M. 231
Boggio, T. 160
Bounds, for eigenvalues 105 119—124
Brunelli, P.E. 142
Caque, J. 42
Carleman, T. 186 231
Carleman, T., (equations of Carleman type) 185 202ff.
Cauchy's formula for determinants 219
Cauchy's principal value of integrals 166
Chandrasekhar, S. 163
Characteristic, of a determinant 59
Closed cycle 22
Closed systems, of functions 90ff.
Collatz, L. 231
Complete systems, of functions 86ff.
Completeness, of the polynomials 96
Completeness, of the trigonometic system 95
Completeness, theorem (Sturm-Liouville systems) 134
composition 10 23ff.
Connecting rod 142
Connection, linear algebraic equations 4 56
Connection, with differential equations 18 127
Continuous spectrum 161
Convergence in tho mean 84
Convolution theorem (Hilbert transformation) 169
Courant, R. 120 123
Courant, R.— Hilbort, D. 123 207 231
Criterions, of completeness 92—95
Critical speeds, of a rotating shaft 1 136 140
Dalzell's criterion of completeness 94
Davis, H.T. 25 40 231
Derivatives of  71
Diagonal, of a kernel 15
Dini, U. 95 126
Dini, U., theorem 126
Dirichlet problem 77
Doetsch, G. 24 231
Duffing, G. 214
Egoroff-Severini theorem 51
Eigenfunctions 59 73ff.
Eigensolutions 133
Eigenvalues 3 31
Eigenvalues, of iterated kernels 74
Eigenvalues, of symmetric kernels 102
Eigenvalues, of symmetric kernels, (bounds for the eigenvalues) 105 119—124
Elliptic integrals 213
Evans, G.C 25 231
Extremal properties of eigenvalues 118
Faltung 23
Faltung, (equations of the Faltung type) 22
First kind, (equations of the first kind) 15 110 143 150
Forced oscillations 213
Fourier coefficients 85ff.
Fourier coefficients, series 87 115
Frank, P.-v.Mises, R. 155 159 229 231
Fredholm, I. 3 5ff.
Fredholm, I., equations 3ff.
Fredholm, I., formulae 66
Fredholm, I., operator 53 137
Fredholm, I., theorems for PG-kernels 63
Fredholm, I., theorems for PG-kernels, for general kernels 65
Fubini, G. 20
Fubini, G., thoorem 9 171
Fubini, theorem, (method of Fubini) 20ff.
Fuchs, L. 42
Functions  57 58 66ff.
Goffman, C 9 51 184 207
Golomb, M. 213
Goursat, E. 231
Greco, D. 146
Green's formula 53
Green's formula, function 130
Green's formula, theorem 156
Gudermannian 30
Hadamard's Theorem 68 223
Hamel, G. 180 214 230 231
Hammerstein, A. 197ff.
Hammerstein, A.(equations of Hammerstein type) 198ff.
Hankel's kernel 163
Hankel's kernel, transformation 164
Hardy, G.H. 171 231
Hardy, G.H., Littlewood, J.E.and Polya, G. 9 170 231
Hellinger, E.and Toeplitz, O. 231
Heywood, H.B.and Fr6chet, M. 232
Hilbert, D. 5 166 232
Hilbert, transformation 167
Hilbert, transformation, (finite Hilbert transformation) 169ff.
Hilbert-Schmidt theorem 11 Off.
Hille, E. 232
Hohenemser, K. 232
Hurwitz's sign 87
Iglisch, R. 146 214
Ince, E.L. 128 135 232
Index, of an eigenvalue 59
Influence function 1 26 136 138
Inversion, of principal integrals 170—172
Jahnke-Emde 30
Janet, M. 232
Kaczmarz, S.,-Steinhaus, H. 82 232
Kellogg 0.D. 78
Kernel(s) 3ff.
Kernel(s), ( kernels and  kernel) 8 10ff.
Kernel(s), (Hermitian kernels) 81
| Kernel(s), (iteratod kernels) 7 50ff.
Kernel(s), (of the form  ) 17
Kernel(s), (of the form  38 152 166
Kernel(s), (of the form k(x-y) 17 23
Kernel(s), (positive kernels) 123 124
Kernel(s), (resolvent kernel) 8 llff.
Kernel(s), (shortened kernel) 124
Kernel(s), (triangular kernel) 116 121 131 138 144 215 228
Kernel(s), of elasticity theory 137
Kernel(s), of Pincherle-Goursat type 55ff.
Kirchhoff, G. 141
Kneser, A. 232
Knopp, K. 96 123 232
Korn, A. 232
Kowalewski, G. 232
Krall, G.and Einaudi, R. 124 160 232
Kupradze, V.O. 197
Lalesco, T. 232
Lalesco-Picard's equation 162
Lancloz, C. 76
Langer, R. 20
Laplace equation 77
Laplace equation, transformation 24
Lebesgue integral 9
Left and right iterated kernels 146—149
Legendre polynomials 99
Linearly independent functions 56
Liouville, J. 42
Lovitt, W.V. 59 74 78 232
Mercer's theorem 125
Method, of Enskog 76 100—102
Method, of Fubini 20 ff.
Method, of Liouville-Stekloff 20
Method, of Ritz 121
Method, of Schmidt-Picone 64
Method, of successive approximations 6 41ff.
Mihlin, S.G. 66 196
Minorsky, N. 47
Miranda, C 146
Morse, Ph.M. 159 232
Muskhelishvili, N.I. 161 197 232
Natural frequencies 120 137 140
Navarro Barras, F. 232
Nazarow, N. 213
Neumann's series 49
Nicholson (formulae of) 36
Non-linear integral equations 42—47 197ff.
Non-linear integral equations, mechanics 47
Norm 9
Normalized functions 60
Numerical solution of intogral equations 75
Numerical solution of intogral equations, evaluation of eigenvalues 31 105 119—124 141 160
Nystroem, E.J. 75
Orthogonal systems of functions 81 ff.
Oscillations of a beam 26 136
Oscillations of a beam, of electrical circuits 47
Oscillations of a beam, of membranes 154
Paley, R.E.A.C.and Wiener, N. 232
Parseval's equation 85
Parseval's equation, generalized 87 168
Peano, G. 42
Pendulum 213
Petrovsky, I.G. 232
Picard, E. 16 42
Picono, M. 64 232
Pinchorle-Goursat kernels 55ff.
Poincare, H. 171
Poisson's integral 144 167
Polya, G.and Szego, G. 160 232
Potentials 78
Prescott, J. 138
Principle, of analytic continuation 52
Principle, of Betti-Maxwell 1 158
Process of orthogonalization 82
Reduction to symmetric kernel 145
Reissner, E. 166
Resolvent kernel 8 11ff.
Resolvent kernel, (equations for the resolvent kernel,) 11 15 52 71
Richard, U. 230
Riesz, F. 233
Riesz-Fischer theorem 88
Saks, S. 9
Sato, T. 43
Schmeidler, W. 233
Schmidt, E. 5 64 147 197 214
Schreier, O.and Sporner, E. 59 60
Schwank, F. 233
Schwarz' inequality 8
Schwarz' inequality, for sums 112
Singular integral equations 40 161ff.
Sohngen, H. 175 179
Spectrum, of a kernel 65 102 161
Stioltjes transformation 184
Stone, M.H. 233
Sturm-Liouville systems 128
Systems, of integral equations 21 40 150
Szego, G. 20 180 233
Tamarkin, J.D. 146
Tautochrone 39
Tchobichef polynomials 180
Titchmarsh, E.0. 24 166 168 176 233
Tonelli, L. 40
Traces, of a kernel 72 114 127
Tricomi, F.G. 20 33 59 60 76 81 82 89 95 130 135 139 141 156 163 169 172 173 180 185 196 214 223 229 230 233
Trivial solutions 55
Trjitzinsky, W.R 161 213
Turning points 33
v.Neumann, J. 232
Vibrating string 31
Vibrations, of a beam 140
Vibrations, of a membrane 154
Vitali criterion 93
Vivanti, G. 233
Vokua, I. 197
Volterra, V. 5ff.
Volterra, V.and Peres, J. 233
Walsh, J.L. 89
Watson, G.N. 34 37 38
Weyl, H. 233
Weyl, lemma 89
Whittaker, E.T.and Watson, G.N. 233
Wiarda, G. 233
Widder, D.V. 24 184 185 233
Wiener, N.and Hopf, E. 163
Wintner, A. 233
Zaanen, A.C 233
Zero-functions 10
Zeros, of Bessel functions 38
|
|
|
| Реклама |
|
|
|
|
|
О проекте