Appell J.M., Kalitvin A.S., Zabrejko P.P. — Partial Integral Operators and Integro-Differential Equations :: Электронная библиотека попечительского совета мехмата МГУ

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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 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:

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

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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