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Appell J.M., Kalitvin A.S., Zabrejko P.P. — Partial Integral Operators and Integro-Differential Equations
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 Equations

Авторы: 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: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 560

Добавлена в каталог: 05.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta_2$ condition      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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