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Appell J.M., Kalitvin A.S., Zabrejko P.P. — Partial Integral Operators and Integro-Differential Equations
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Название: Partial Integral Operators and Integro-Differential EquationsАвторы: Appell J.M., Kalitvin A.S., Zabrejko P.P.Аннотация: Three authors, from Germany, Russia, and Belorussia, examine the two related notions. They describe partial integral operators as linear or nonlinear operators with integrals that depend on a parameter. The integro-differential equations are of the Barbashin type in that the right-hand sides contain both a multiplication operator and an integral operator. The connection, they explain, is that an initial value problem for a Barbashin integro-differential equation, linear or nonlinear, leads in a natural way to a fixed-point problem involving a partial integral operator. Drawing on research in Russia much of which has not even been referenced in the west, they cover first the equations of the Barbashin type and the theory behind them, then the operators. They close with generalizations and applications of each.
Язык: Рубрика: Математика /Анализ /Дифференциальные уравнения /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2000Количество страниц: 560Добавлена в каталог: 05.04.2005Операции: Положить на полку |
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Предметный указатель
90 Absolutely bounded set 77 Absolutely continuous norm 77 89 Adjoint operator 61 222 Aerodynamics 480 Algebraic multiplicity 288 Associate operator 61 222 Associate space 61 221 Astrophysics 444 Averaging method 7 Banach — Caccioppoli theorem 141 Barbashin equation 18 Barbashin equation, generalized 360 Barbashin equation, homogeneous 18 Barbashin equation, nonhomogeneous 18 Barbashin operator 1 18 Barbashin operator, generalized 360 371 Barbashin operator, non-stationary 3 Barbashin operator, stationary 3 Bochner space 193 Bogoljubov space 157 Bogoljubov theorem 130 158 Boundary condition 179 Boundary value problem 179 201 372 Bounded solution 336 Boussinesq approximation 484 Boussinesq equation 428 Cantilever method 482 Category inclusion 227 Cauchy operator 2 Characteristic function 59 280 Characteristic operator 68 Chebyshev space 19 Compact operator 43 Condensing operator 141 Conditional distribution function 422 Cone-positive eigenvalue 323 Conic interval 59 Contact problem 467 Continuous dependence 126 Continuous media 459 Continuous solution 336 Contracting operator 141 193 Counting measure 217 Creeping 472 Critical point 389 Crossnorm 290 Crossnorm, quasi-uniform 290 Crossnorm, uniform 290 Darbo theorem 142 161 Defect spectrum 287 Degenerate kernel 29 167 Density function 432 Discriminant 196 209 Distribution function 426 Distribution function, conditional 422 Dual space 61 Dunford-Pettis theorem 43 Eigenfunction 343 Eigenvalue 287 343 Eigenvalue, cone-positive 323 Elasticity 450 Equation, Barbashin 18 Equation, Boussinesq 428 Equation, Euler 483 Equation, Gel'fand — Levitan 487 Equation, Hammerstein 378 Equation, Kolmogorov — Feller 425 445 Equation, Korteweg — de Vries 428 Equation, Lipman — Schwinger 486 Equation, Markov 421 Equation, Navier — Stokes 487 Equation, Predholm 328 Equation, reduced 2 Equation, Schrodinger 428 Equation, Uryson 366 Equation, Volterra 334 Equation, Volterra — Fredholm 463 Essential infimum 100 122 Essential range 102 Essential spectrum 102 288 Essential spectrum in Browder's sense 288 Essential spectrum in Kato's sense 288 Essential spectrum in Schechter's sense 102 288 Essential spectrum in Wolf's sense 102 288 Essential supremum 38 Euler equation 483 Evolution equation 427 Evolution operator 2 3 24 49 82 100 363 Exponent, Ljapunov 7 115 Exponent, Ljapunov — Bohl 7 Exponential dichotomy 154 Exponential operator 25 Fatou property 90 Fixed point theorem 140 Fixed point theorem in if-normed spaces 193 Fixed point theorem, Banach — Caccioppoli 141 Fixed point theorem, Darbo 142 161 Fixed point theorem, Sadovskij 143 Fixed point theorem, Schauder 141 Fourier transform 356 Fracture mechanics 472 Frechet derivative 394 Fredholm alternative 165 462 Fredholm equation 328 Fredholm operator 462 Fredholm operator of index zero 462 Fredholm point 102 Fredholm point of index zero 102 Function, characteristic 59 280 Function, fundamental 87 Function, Green 7 153 155 Function, impuls-transition 483 Function, integral-bounded 381 Function, Ljapunov 120 Function, majorant 148 Function, minorant 150 Function, permutable 430 Function, weakly continuous 259 Function, weakly semicontinuous 389 Function, Young 91 242 Fundamental function 87 Gel'fand formula 109 Gel'fand — Levitan equation 487 Generalized solution 20 Glueing condition 180 Green function 7 153 155 Grothendieck theorem 43 Growth function 405 Hamiltonian system 430 Hammerstein equation 378 Hammerstein operator 378 Holder continuity 139 Ideal space 85 Ideal space with mixed norm 229 Ideal space, almost perfect 90 Ideal space, perfect 90 Ideal space, quasi-regular 89 Ideal space, regular 89 Ideal space, weighted 87 Impulse transition function 483 INDEX 288 313 462 Infra-stamping operator 54 Initial condition 2 4 Initial value problem 2 4 367 Integral operator 2 4 Integral-bounded function 381 Interpolation theory 56 71 Inverse problem 431 487 K-norm 192 209 371 k-space 192 209 Kernel 3 29 31 Kernel, degenerate 29 167 Kernel, positive 322 kernel, symmetric 31 Kimura model 433 Kolmogorov — Feller equation 425 445 Korteweg-deVries equation 428 Kothe adjoint 61 Kothe dual 61 477 Krasnosel'skij-Ladyzhenskij lemma 390 Laplace transform 356 Lebesgue space 19 Lebesgue space with mixed norm 8 237 Limit spectrum 287 Lipman — Schwinger equation 486 Ljapunov exponent 7 113 Ljapunov function 120 Ljapunov-Bohl exponent 7 113 Lorentz space 87 Majorant function 148 Marcinkiewicz space 87 Markov equation 421 Markov process 421 444 Maximal monotone operator 385 Measure of a set 108 Measure of an operator 108 Measure of noncompactness 108 141 Minor ant function 150 Mixed norm 8 69 70 243 Mixed problem 463 Module 58 Monotone operator 385 Monotonicity principle 385 Multiplication operator 2 3 Multiplicator space 224 Multiplier 3 21 179 Mutation rate 434 n-absolutely bounded set 77 Navier — Stokes equation 487 Nemytskij operator 11 387 Nemytskij operator, generalized 403 Neumann series 158 Neutron transfer 439 Newton — Kantorovich method 394 Norm, absolutely continuous 89 Operator algebra 37 62 98 224 268 operator function 45 47 251 255 276 Operator function, absolutely norm-continuous 255 Operator function, absolutely strongly continuous 255 Operator function, non-stationary 3 Operator function, norm-continuous 47 76 Operator function, stationary 3 Operator function, strongly continuous 45 74 Operator ideal 37 62 98 224 268 Operator, adjoint 61 222 Operator, associate 61 222 Operator, Barbashin 1 18 Operator, Cauchy 2 Operator, characteristic 68 Operator, compact 43 Operator, condensing 141 Operator, contracting 141 193 Operator, evolution 2 3 24 49 82 100 363 Operator, exponential 25 Operator, Fredholm 462 Operator, Hammerstein 378 Operator, infra-stamping 54 Operator, integral 2 4 Operator, maximal monotone 385 Operator, monotone 385 Operator, multiplication 2 3 Operator, Nemytskij 11 387 Operator, Poincare 162 Operator, projection 68 154 305 Operator, regular 58 63 224 Operator, shift 162 Operator, stamping 52 Operator, u-bounded 72 Operator, Uryson 366 Operator, v-cobounded 72 Operator, Volterra 357 Operator, Volterra — Fredholm 463 Operator, Volterra-like 141 Operator, weakly coercive 385 Operator, weakly compact 43 69 Order complete space 192 Order convergence 192 Orlicz space 86 Orlicz space with mixed norm 242 Parameter, essentially distributed 432 Parameter, spatially distributed 432 Partial integral equation 328 354 Partial integral equation of Fredholm type 328 Partial integral equation of Volterra type 328 Partial integral operator 4 Partial integral operator of Fredholm type 328 Partial integral operator of Romanovskij type 350 Partial integral operator of Volterra type 334 Periodic solution 140 Permutable function 430 Perturbation of the Green function 145 Perturbation of the Ljapunov — Bohl exponent 114 Poincare operator 162 Point spectrum 287 Poisson coefficient 451 Positive kernel 322 Potential 389 probability density 433 Projection operator 68 154 305 Quadratic functional 121 Radiation propagation 439 Radon representation 35 Radon theorem 34 Random process 421 Random variable 421 Reduced equation 2 Reflexive space 385 Regular operator 58 53 224 Regular part 89 Resolvent set 287 Resolvent set, regular 299 Riesz criterion 36 Rigidity 451 Sadovskij theorem 143 Scattering 439 Schauder theorem 141 Schrodinger equation 428 Set, absolutely bounded 77 Set, n-absolutely bounded 77 Shift operator 162 Sign condition 207 Smooth dependence 137 Solution, bounded 336 Solution, continuous 336 Solution, generalized 20 Solution, periodic 140 Space of countable type 59 Space of type L 94 Space with mixed norm 8 243 Space, associate 61 221 Space, Bochner 193 Space, Bogoljubov 157 Space, Chebyshev 19 Space, dual 61 Space, ideal 85 Space, Lebesgue 19 Space, Lorentz 87 Space, Marcinkiewicz 87 Space, multiplicator 224
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