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Tricomi F.G. — Integral equations
Tricomi F.G. — Integral equations

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Название: Integral equations

Автор: Tricomi F.G.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1957

Количество страниц: 246

Добавлена в каталог: 11.05.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 ${L}_{2}$-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 $\mathscr D(\lambda)$      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 ${\mathscr D}(\lambda),\;{\mathscr D}(x,y;\lambda)$      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), (${L}_{2}$ kernels and ${L}_{2}^{*}$ kernel)      8 10ff.
Kernel(s), (Hermitian kernels)      81
Kernel(s), (iteratod kernels)      7 50ff.
Kernel(s), (of the form $A(x)/B(y)$)      17
Kernel(s), (of the form ${F.|x - y|}^{-\alpha}$      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
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