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| Volterra V. — Theory of Functionals and of Integral and Integro-Differential Equations |
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| Предметный указатель |
Abel 55 56 69
Adams 176 208
Addition theorems, Huygens' principle in Hadamard's sense 183
Addition theorems, integral addition theorems 105 133
Addition theorems, integral addition theorems connected with the equations of mathematical physics 183
Alexandroff 205 208
Amoroso 167 206 208
Andreoli 134 208
Arzela 13 35 173
Baer 208
Baeri 167
Baire 8 14 35
Banach viii 208
Barnet 167
Barnett 208
Bateman 208
Bedarida 167
Bennett 69
Bernstein 69
Bertrand 208
Bianchi 103
Birkhoff 208
Birtwistle 200 217
BLISS 206 208
Block 69
Bocher vi 50 69 181
Bocher's type of integro-differential equations 181
Bohannan 97
Boltzmann 208
Bompiani 135
Bonferroni 208
Born 208
Bouligand 35 181 208
Bourlet 201 208
Bray 180 181 182 208
Browne 69
Bucht 69
Burgatti 69
Calculus of variations as a chapter of theory of functionals 13 14 172
Calo 200 209
Castigliano 187
Cauchy 74 87 95 103 131 183 192
Chrystal 209
Composition, composition of the first kind 99
Composition, composition of the second kind 100
Continuity of functionals 9—14
Courant vii 24 35 209
Cramer 44 48 49
Crudeli 167
D'Alembert 149
Daniele 35 135 167
Daniell 34 35
Davis 69 174 209
de Donder 97 217
De Toledo v ix
Delsarte vi 185 186 209
Derivatives, derivative by composition 129
Derivatives, derivatives of functions of lines with respect to the coordinate planes 80
Derivatives, derivatives with any index whatever 55
Derivatives, differentiation, derivation, variation of functionals 22—25
Derivatives, necessary and sufficient condition that a functional may be considered as the functional derivative of another functional 157—159
Derivatives, symmetry of derivatives of functionals 24
Dienes 35
Dines 209
Dirichlet 4 46 47 56 57 165 173 174 175 181 182
Dirichlet's problem, Evans' method in the case of discontinuous boundary value problems 180—181
Dirichlet's problem, method of integral equations 174—175
Dirichlet's problem, method of the calculus of variations and functions of lines 173
Dixon 69
Donati 187 217
Euler 31 127 160
Euler's theorem on homogeneous functions (Extension of) 160
Evans v vi vii viii 35 47 58 68 69 70 101 134 135 154 155 167 168 180 181 182 206 208 209
Evans' boundary value problems for Poisson's equation 181 see
Fabri 6 36 79
Fantappie v vi ix 53 70 184 200 201 202 203 204 209 210
Fantappie's functional indicatrix 201—203
Fischer 36 168
Forel 177 210
FOURIER 154 176
Frank 210
Frechet vi 8 9 10 13 15 20 21 27 29 36 97 156 168 202 204 205 210 211 218
Frechet's abstract aggregates, abstract spaces 8—14 204—205
Freda viii 160 161 168
Freda's functional derivative equations 160
Fredholm 49 62 70 175 176 184 185 186 204 211
Fubini 168
Fuchs' theory of linear differential equations (Extension of) 141
Functional derivative equations in the theory of isogeneity 90—95
Functional derivative equations of the first order, canonical integro-differential equations and connected functional derivative equation 163
Functional derivative equations of the first order, functional derivative equations in functions of lines 82 88 155 156 see
Functional derivative equations of the first order, functional derivative equations of the first order and connected integro-differential equations 161
Functional derivative equations of the second order, equations in quantum electrodynamics 165
Functional derivative equations of the second order, equations of Laplace type 164
Functional equations, branch elements of solutions of functional equations 65—66
Functional equations, general functional equations and implicit functionals 63—65
Functional equations, generalisations of systems of n equations in n unknowns 40
Functionals, analytic functionals 201
Functionals, extremes of a functional 13
Functionals, functional derivative equations 155
Functionals, functional dynamics 184
Functionals, functional fields 7
Functionals, functional operators 8 200
Functionals, functional power series 21
Functionals, functional rotations 185
Functionals, functional transformations 183
Functionals, functionals in quantum mechanics 208
Functionals, functionals in the theory of elasticity 187 see
Functionals, functionals of degree n 19
Functionals, functionals of the first degree 14
Functions of an infinite number of variables and problems with an infinite number of unknowns 2 3 22 23 40 43 49 138 158 161 163 176 179—180 184—185 203
Functions, conjugate functions in space 87—90
Functions, functions by composition 129 132
Functions, functions of hyperspaces 6 85
Functions, functions of lines 59 74
Functions, functions of lines of the first degree 79
Functions, isogenic functions 91—95
Functions, order of a function 110
Gateaux vii 12 33 36 37 164 187
Gauss 89 173
Giorgi 200 211 217 218
Goursat 50 51 52 70 176
Graffi 149 171 196
Gramegna 168
Graustein 97
Green vii 89 152 153 165 166 174 179 181
Green's function in integro-differential equations (Extension of) 153 see
Groups (Functional), group of the functions permutable with a given function 110
Groups (Functional), groups in functional kinematics 185
Groups (Functional), groups of linear functional transformations 183—184
Groups (Functional), invariant for groups of functional transformations 184
hadamard vii 13 15 16 37 55 70 103 105 124 133 135 166 168 173 183 184 202 203 211
Hadamard's differential equation for Green's function 166
Hadamard's differential equation for Green's function, expression for linear functionals 15 see
Hamilton 156 163 164 172
Heaviside 200 218
Hebroni 168
Hecke 211
Heisenberg 164 173 208 211
Helly 37
Hereditary questions, energy equations in hereditary phenomena 196—200
Hereditary questions, general laws of heredity 188—190
Hereditary questions, hereditary action in elastic torsion 147—149 189
Hereditary questions, hereditary dynamics 191
Hereditary questions, hereditary elasticity 192
Hereditary questions, hereditary electromagnetism 194
Hereditary questions, hereditary phenomena 147
Hereditary questions, principle of the closed cycle 189
Hereditary questions, principle of the dissipation of hereditary action 188
Hertz 194 211
| hilb 168
hilbert vii 50 51 70 173 175 176 203 204 212
Hildebrand 37
Hill 168
Hirahawa 212
Holmgren 55 70
Hooke 193 194
Horn 70
Hostinsky 166 212
Hotelling 206 212
Hu (Minfu Tat) 168
Huygens 183 184
Ince 70
Integral equations, applications of the theory of composition to the solution of integral equations 106 143 145
Integral equations, Fredholm's integral equations 41
Integral equations, Fredholm's linear integral equations of the first kind 51
Integral equations, Fredholm's linear integral equations of the second kind 48
Integral equations, integral equations obtained from problems of the calculus of variations 30 141
Integral equations, inversion of multiple integrals 63
Integral equations, systems of integral equations 62
Integral equations, Volterra's integral equations 42
Integral equations, Volterra's linear integral equations of the first kind 53
Integral equations, Volterra's linear integral equations of the second kind 43
Integration of functionals 32
Integro-differential equations, equations of canonical type 163 see
Integro-differential equations, generalisation of systems of n differential equations with n unknown functions 138
Integro-differential equations, integro-differential equations for biological species living together 206
Integro-differential equations, integro-differential equations for the determination of groups of permutable functions 112 142
Integro-differential equations, integro-differential equations obtained from problems of the calculus of variations 31 142
Integro-differential equations, integro-differential equations obtained from the theory of permutable functions of the first kind 143—145
Integro-differential equations, integro-differential equations obtained from the theory of permutable functions of the second kind 145—147
Integro-differential equations, integro-differential equations of elliptic, hyperbolic, and parabolic type 149—155
Integro-differential equations, systems of integro-differential equations 145
jacobi 155 156 163
Jacobi — Hamilton theory (Extension of the) 156
JORDAN 164 165 168 176
Joule 199
Kakeya 37 70
Kellogg 208 212
Kernels, case in which the kernel vanishes 60
Kernels, Evans' method by calculation of solvent kernels 67
Kernels, Evans' periodic kernels 134
Kernels, kernels of the closed cycle 189
Kernels, logarithmic kernels 58
Kernels, singular kernels 54 58
Kernels, solvent kernels 44 67
Kernels, symmetrical kernels 50
Korn 212 218
Kostitzin 195 212
Kowalewski 183 184 212
Krall 166 168
Lagrange 74 179 185 191 200
Lalesco 50 61 70 176
Laplace 86 88 89 90 92 150 153 164 174 181
Lauricella 53 70 135 212
Le Roux 70
Le Stourgeon 37
Lebesgue 9 37 132 135
Lefschetz 85 97
Leibniz 200 218
Lense 212
Levi 37 213
Levi-Civita 70 184 213
Levy (P.) vi vii 11 12 18 37 70 71 159 166 169 205 213
Lichtenstein 213
Lie 184
Liouville 55 56 71
Lipschitz 140
Logarithms by composition 124
Luesis 135
Mandelbrojt 56 71 95 97
Manneback 213
Marcolongo 213
Maria 180 213
Marian 177 213
Matteuzzi 180 213
Michal vi 184 213 214
Miles 182
Moisil vi 185 214
Molinari 71
Moore vi 204 214
Morera 95 218
Myller 214
Nalli 38 136
Neumann 175 178 182
Nicholson 214
Nicolesco 74 97
NOERLUND 136
Oseen 214 218
Pascal (E.) 38 97
Pascal (M.) 97
Pauli 164 165 168 173 176 211
Peano 173 214
Peres vi viii 101 106 110 111 112 113 114 115 116 117 118 121 122 123 126 129 130 131 136 169 182
Peres' transformations 114—118
Permutability, determination of the functions permutable with a given function 110—114 see
Permutability, functions permutable of the first kind with unity 108—110
Permutability, permutability of the first and of the second kind 100
Picard 42 53 71 139 214
Pick 214
Picone 38 71 214
Pincherle 200 201 202 214 215 218
Poincare 175 180 215
poisson 164 181
Poisson's parentheses (Extension of) 164
Poli 71
Polydromy of function of lines 82—85
Pomey 141 169
Poole 215
Popovici 176 215
Powers, powers and polynomials by composition 101
Powers, powers by composition with a fractional exponent 118
Powers, powers by composition with a negative exponent 122—124
Poynting 198 215
Prasad 71
Proudman 179 215
Radon 38
Rasor 38
Recchia 136
Ricci 176
Richardson 215
Riemann 55 71 74 86 173
Riesz 17 38
Risser 206 215
Roos 206 215
Roster 215
Sabbatini 66 71
Sassmannshausen 170
Sbrana 71 215
Scatizzi 55 72
Schlesinger 141 170
Schmidt 51 65 72 176
Schoenbaum 170 206 215
Schroedinger 165
Schwarz 173 215
Seiches (Oscillations of lakes) 170 177
Series, series by composition of the first kind 102
Series, series by composition of the second kind 132
Serini 195 216
Servois 200
Severini 136
Sierspinski 205 216
Sinigallia 136 170
Somigliana 166
Sonine 56 72
Staeckel 164
Staeckel's theorem of the separation of the variables (Extension of) 164
Steinhaus viii 15 38 218
Stieltjes 9 17 18 34 182
Stokes 158 159
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