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Volterra V. — Theory of Functionals and of Integral and Integro-Differential Equations
Volterra V. — Theory of Functionals and of Integral and Integro-Differential Equations

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Название: Theory of Functionals and of Integral and Integro-Differential Equations

Автор: Volterra V.

Аннотация:

A general theory of the functions depending on a continuous set of values of another function, this volume is based on the author's fundamental notion of the transition from a finite number of variables to a continually infinite number. Deals primarily with integral equations, and also addresses the calculus of variations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1930

Количество страниц: 240

Добавлена в каталог: 19.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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