Gripenberg G., Londen S.O., Staffans O. — Volterra integral and functional equations :: Электронная библиотека попечительского совета мехмата МГУ

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Gripenberg G., Londen S.O., Staffans O. — Volterra integral and functional equations

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Название: Volterra integral and functional equations

Авторы: Gripenberg G., Londen S.O., Staffans O.

Аннотация:

The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations. The book is divided into three parts. The first considers linear theory and the second deals with quasilinear equations and existence problems for nonlinear equations, giving some general asymptotic results. Part III is devoted to frequency domain methods in the study of nonlinear equations. The entire text analyzes n-dimensional rather than scalar equations, giving greater generality and wider applicability and facilitating generalizations to infinite-dimensional spaces.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 725

Добавлена в каталог: 24.08.2014

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Предметный указатель

Resolvent, resolvent continued real-valued      44
Resolvent, size of $L^{1}$ -norm      59[2.6.1]
Resolvent, totally positive type      626[20.4.11]
Resolvent, type $B^{\infty}$       244[9.5.4]
Resolvent, type $B^{\infty}_{0}$       248[9.6.3]
Resolvent, type $L^{1}$       258[9.8.5] 270[9.9.2]
Resolvent, type $L^{p}$       19[1.3.9] 232(9.3.1] 234(9.3.6] 235[9.3.9] 235[9.3.10] 236[9.3.13] 238[9.3.14] 238[9.3.15] 238[9.3.16] 239[9.3.19] 258[9.8.3]
Resolvent, type $L^{p}_{loc}$       241 [9.4.2] 241(9.4.3] 260(9.8.6] 399[13.3.2]
Resolvent, type $L^{\infty}$       244[9.5.4] 258[9.8.5]
Resolvent, type $[B^{\infty};\mathcal{T}_{S}]$       251[9.6.10]
Resolvent, type $[C;\mathcal{T}_{S}]$       251[9.6.10]
Resolvent, type BC      244[9.5.4]
Resolvent, type BUC      244[9.5.4] 245[9.5.5] 265[9.9.1]
Resolvent, type C      245[9.5.5]
Resolvent, unbounded      195 [7.2.4]
Resolvent, unique      42[2.3.1] 46[2.4.3] 49[2.4.7] 114[4.1.5] 125[4.4.4] 233[9.3.3] 287
Resolvent, used in a perturbed linear equation      313 317 334
Resolvent, Volterra resolvent      232(9.3.1] see
Resolvent, whole line      46[2.4.3] 47(2.4.4] 125(4.4.4] 126(4.4.5] 196(7.2.4]
Resolvent, zero at infinity      62[2.6.6]
Riemann — Lebesgue lemma      41 52[2.5.4]
Riesz' criterion for total boundedness      373
Riesz' interpolation theorem      231 623
S, S'      xix 495—496 499 527 528
Sard's theorem      481[15.8.2] 591
Schauder's theorem      314 342 347[12.1.4] 632 see
Second kind      see "Volterra equation
Self-adjoint matrix      see "Matrix self-adjoint"
Semi-inner product      525 526[16.7.1]
Semigroup      207
Semigroup, adjoint      213 213[8.2.8] 216[8.3.5]
Semigroup, equivalence      213 214[8.2.9] 217[8.3.6]
Semigroup, extended forcing function semigroup      216[8.3.4]
Semigroup, extended initial function semigroup      215[8.3.2]
Semigroup, forcing function semigroup      210[8.2.4] 211
Semigroup, infinitesimal generator      208 210[8.2.5] 211 218[8.3.7] 218[8.3.8]
Semigroup, initial function semigroup      209[8.2.2] 210[8.2.5]
Semigroup, spectrum of an infinitesimal generator      213[8.2.7] 219
Semigroup, strongly continuous      208 209[8.2.1] 209[8.2.3] 215[8.3.1] 216(8.3.3]
Semigroup, transposed forcing function semigroup      210[8.2.4]
Semigroup, transposed initial function semigroup      209[8.2.2]
Semigroup, true adjoint      221
Shea — Wainger theorem      169[6.2.1]
Singular part expansion      193
Solution of a linear equation, continuous dependence      236[9.3.12] see continuous "Resolvent continuous
Solution of a linear equation, exponential polynomial plus remainder      194[7.2.3] 197[7.2.5]
Solution of a linear equation, exponentially growing      18[1.3.7] 194[7.2.3] 197[7.2.5]
Solution of a linear equation, nonnegative      263 [9.8.7]
Solution of a linear equation, rate of convergence      22[1.3.11]
Solution of a linear equation, unbounded      194[7.2.3] 197[7.2.5]
Solution of a linear equation, unstable      195 197
Solution of a linear equation, variation of constants formula, differential resolvent equation      299[10.4.1]
Solution of a linear equation, variation of constants formula, equation in an associative algebra      233[9.3.4] 234[9.3.5]
Solution of a linear equation, variation of constants formula, equation of the first kind      17[1.3.5] 157 158[5.5.3]
Solution of a linear equation, variation of constants formula, integral equation      14[1.3.2] 16[1.3.4] 36 44[2.3.5] 114[4.1.7] 128[4.4.10]
Solution of a linear equation, variation of constants formula, integrodifferential equation      15[1.3.3] 77 78 81[3.3.3] 131[4.4.17]
Solution of a linear equation, variation of constants formula, nonconvolution equation      226 234[9.3.6] 241 244[9.5.4] 246[9.5.6]
Solution of a linear equation, variation of constants formula, nonconvolution equation with measure kernel      20[1.3.10] 288[10.2.5] 290[10.2.12]
Solution of a linear equation, variation of constants formula, nonconvolution integrodifferential equation      21 [1.3.10] 297[10.3.9] 303[10.4.6]
Solution of a linear equation, variation of constants formula, periodic      49[2.4.7] 88[3.3.11]
Solution of a nonlinear equation      348 see
Solution of a nonlinear equation in a cone      627[20.4.12] see maximal"
Solution of a nonlinear equation, $(t,x(t))\in D\cap K$       353[12.2.4] 358[12.2.9]
Solution of a nonlinear equation, $(t,x(t))\in K$       368[12.4.7]
Solution of a nonlinear equation, $x - Ag\circ x\in BC(R^{+})$       569[18.3.1] 571[18.3.2]
Solution of a nonlinear equation, $x - Ag\circ x\in L^{2}(R^{+})$       569[18.3.1] 571[18.3.2]
Solution of a nonlinear equation, $x\in BC(R^{+};\varphi)$       323[11.3.3]
Solution of a nonlinear equation, $x\in L^{2}(R^{+})$ , integral equation      332[11.6.2] 333[11.6.3] 554[17.5.1] 555[17.5.2] 556[17.5.4] 567[18.2.4] 575[18.4.3] 579[18.4.8] 580[18.4.9] 585[18.6.1]
Solution of a nonlinear equation, $x\in L^{2}(R^{+})$ , integrodifferential equation      334[11.6.4] 549[17.4.1] 551[17.4.3] 565(18.2.1]
Solution of a nonlinear equation, $x\in L^{2}(R^{+})$ , remoulded equation      577[18.4.5] 577[18.4.7]
Solution of a nonlinear equation, $x^{'}\in L^{2}(R)$       599[19.3.2]
Solution of a nonlinear equation, $x^{'}\in L^{2}(R^{+})$       545[17.3.2] 549[17.4.1] 551[17.4.3] 558[17.6.4] 567[18.2.4] 648[20.6.1]
Solution of a nonlinear equation, $x^{'}\in L^{\infty}(R^{+})$       544[17.3.1]
Solution of a nonlinear equation, $|x(t)|\leq\delta e^{-\epsilon t}$       335[11.7.1]
Solution of a nonlinear equation, asymptotic equivalence      328[11.4.3] 336[11.7.3] 630[20.4.14]
Solution of a nonlinear equation, asymptotically periodic      631[20.4.15]
Solution of a nonlinear equation, asymptotically slowly varying      545[17.3.2] 549[17.3.8] 591[19.2.1] 598(19.3.1] 605[19.4.2] 609[19.4.5] 611[19.5.1] 640[20.5.2] 644[20.5.4]
Solution of a nonlinear equation, asymptotically stable      426
Solution of a nonlinear equation, bounded, differential-delay equation      427[14.2.1] 430[14.2.7] 448[14.5.9]
Solution of a nonlinear equation, bounded, integral equation      317[11.3.1] 319[11.3.2] 336[11.7.3] 444[14.5.1] 555[17.5.3] 556[17.5.4] 567[18.2.4] 567[18.2.5] 567[18.2.6] 569[18.3.1] 573[18.3.4] 580[18.4.9]
Solution of a nonlinear equation, bounded, integrodifferential equation      328[11.4.3] 336[11.7.4] 432[14.2.9] 445[14.5.3] 445[14.5.4] 540[17.2.1] 541[17.2.2] 543[17.2.3] 543[17.2.4] 544[17.2.5] 557[17.6.1] 557[17.6.2] 558[17.6.3] 565[18.2.1] 566[18.2.2] 566[18.2.3] 582[18.5.3] 584[18.5.6] 609[19.4.6]
Solution of a nonlinear equation, bounded, nonconvolution equation      620(20.3.1] 622[20.3.2] 628(20.4.13]
Solution of a nonlinear equation, bounded, nonconvolution integrodifferential equation      619[20.2.5]
Solution of a nonlinear equation, bounded, nonseparable convolution equation      640[20.5.2] 644[20.5.4]
Solution of a nonlinear equation, bounded, remoulded equation      573[18.3.3] 577[18.4.7] 582[18.5.2] 584[18.5.5]
Solution of a nonlinear equation, continuation of      343
Solution of a nonlinear equation, continuous dependence      23[1.3.13]
Solution of a nonlinear equation, continuous dependence, functional differential equation      392[13.2.3]
Solution of a nonlinear equation, continuous dependence, functional equation      386[13.2.1] 393[13.2.4]
Solution of a nonlinear equation, continuous dependence, integral equation      384[13.1.1] 391[13.2.2]
Solution of a nonlinear equation, continuous dependence, integrodifferential equation      327[11.4.3]
Solution of a nonlinear equation, differentiable      401 [13.3.3]
Solution of a nonlinear equation, differentiable with respect to a parameter      23[1.3.13]
Solution of a nonlinear equation, differentiable with respect to a parameter, functional equation      396[13.3.1] 399[13.3.2]
Solution of a nonlinear equation, differentiable with respect to a parameter, integral equation      385[13.1.2]
Solution of a nonlinear equation, enlarged sense      23[1.3.12] 372
Solution of a nonlinear equation, exists, $g(\cdot,x(\cdot))\in L^{2}(R^{+})$       554[17.5.1] 555[17.5.2]
Solution of a nonlinear equation, exists, $g\circ x\in L^{2}(R)$       599[19.3.2]
Solution of a nonlinear equation, exists, $g\circ x\in L^{2}(R^{+})$       557[17.6.1] 565[18.2.1] 567[18.2.4] 573[18.3.3] 573[18.3.4] 575[18.4.2] 575[18.4.3] 577[18.4.5] 579[18.4.8]
Solution of a nonlinear equation, exists, $g^{'}(x(\cdot))x^{'}(\cdot)\in L^{2}(R^{+})$       573[18.3.4]
Solution of a nonlinear equation, exists, $lim_{t\to \infty}(x(t)-y(t))=0$       336[11.7.3]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(a+A\delta,g(\cdot,x(\cdot)),T)<\infty$       554[17.5.1]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(a,g(\cdot,x(\cdot)),T)<\infty$       555[17.5.2] 556[17.5.4]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(b+A\delta,g\circ x,T)<\infty$       575[18.4.2]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(b,(c\ast g\circ x)^{'}+g\circ x,T)<\infty$       577[18.4.5] 579[18.4.8]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(b,g^{'}(x(\cdot))x^{'}(\cdot)+rg(x(\cdot)),T)<\infty$       573[18.3.3] 573[18.3.4]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(b,g^{'}(x(\cdot))x^{'}(\cdot),T)<\infty$       569[18.3.1] 571[18.3.2]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(qa+\mu+A\delta,g\circ x,T)<\infty$       567[18.2.4] 567[18.2.5] 567[18.2.6]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(\mu+c\ast\mu,g\circ x,T)<\infty$       582[18.5.3]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(\mu,g\circ x,T)<\infty$       540[17.2.1] 541[17.2.2] 543[17.2.4] 544[17.2.5] 557[17.6.1] 557[17.6.2] 558[17.6.3] 582[18.5.2]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(\nu+A\delta,g\circ x,T)<\infty$       565[18.2.1] 566[18.2.2] 566[18.2.3]
Solution of a nonlinear equation, exists, $sup_{T>0}Q(\nu,g\circ x+(c\ast g\circ x)^{'},T)<\infty$       584[18.5.5] 584[18.5.6]
Solution of a nonlinear equation, exists, $sup_{t\in R^{+}}|x(t)|\leq\delta$       317[11.3.1] 325[11.4.1] 327[11.4.2] 331[11.5.1] 335[11.7.2]
Solution of a nonlinear equation, exists, $sup_{t\in R}|x(t)|\leq\delta$       319[11.3.2] 337[11.7.5]
Solution of a nonlinear equation, exists, functional differential equation      23[1.3.12] 360[12.3.1]
Solution of a nonlinear equation, exists, functional equation      22[1.3.12] 349[12.2.1] 352[12.2.2] 353[12.2.3] 353[12.2.4] 355[12.2.5] 362[12.4.1] 364[12.4.2] 378

Solution of a nonlinear equation, exists, integral equation      22[1.3.12] 317[11.3.1] 319[11.3.2] 324[11.3.4] 332[11.6.2] 333[11.6.3] 335[11.7.1] 335[11.7.2] 343[12.1.1] 345[12.1.2] 357[12.2.7] 357[12.2.8] 358[12.2.9] 364[12.4.3] 365[12.4.4] 368[12.4.7] 368[12.4.8] 369[12.4.9] 372[12.5.1] 411[13.5.4] 585[18.6.1]
Solution of a nonlinear equation, exists, integral equation, integrodifferential equation      325[11.4.1] 327[11.4.2] 328[11.4.3] 336[11.7.4] 337[11.7.5] 360[12.3.2]
Solution of a nonlinear equation, exists, integral equation, perturbed ordinary differential equation      331 [11.5.1]
Solution of a nonlinear equation, exists, leaves compact sets, functional differential equation      360[12.3.1]
Solution of a nonlinear equation, exists, leaves compact sets, functional equation      349[12.2.1] 352[12.2.2] 353[12.2.3] 354[12.2.4] 355[12.2.5] 364[12.4.2]
Solution of a nonlinear equation, exists, leaves compact sets, integral equation      356[12.2.6] 357[12.2.7] 358[12.2.8] 358[12.2.9] 364[12.4.3] 368[12.4.8]
Solution of a nonlinear equation, exists, leaves compact sets, integrodifferential equation      360[12.3.2]
Solution of a nonlinear equation, exists, limit at infinity      328[11.4.3] 434[14.3.1] 436[14.3.5] 438[14.3.8] 440[14.3.9] 446[14.5.5] 446[14.5.7] 447[14.5.8] 448[14.5.9] 545[17.3.3] 547 559[17.6.4] 575[18.4.3] 577[18.4.5] 579[18.4.8] 591[19.2.1] 598(19.3.1] 611 640[20.5.2] 644[20.5.4] see zero
Solution of a nonlinear equation, exists, Lipschitz-dependence on forcing function      317[11.3.1] 319[11.3.2] 324[11.3.4] 332[11.6.2] 333[11.6.3]
Solution of a nonlinear equation, exists, maximal      403[13.4.2] 403[13.4.3] 406[13.4.6] 407[13.4.8] 408[13.4.9]
Solution of a nonlinear equation, exists, minimal      403[13.4.2] 403[13.4.3] 406[13.4.6] 407[13.4.8] 408[13.4.9]
Solution of a nonlinear equation, exists, noncontinuable      343 see leaves
Solution of a nonlinear equation, exists, noncontinuable, functional differential equation      393[13.2.3] 407[13.4.8] 408[13.4.9]
Solution of a nonlinear equation, exists, noncontinuable, functional equation      376[12.6.2] 386[13.2.1] 393[13.2.4] 396[13.3.1] 399[13.3.2] 404[13.4.3]
Solution of a nonlinear equation, exists, noncontinuable, integral equation      384[13.1.1] 392[13.2.2] 406[13.4.6]
Solution of a nonlinear equation, exists, nonnegative      622 [20.3.2]
Solution of a nonlinear equation, exists, periodic      337(11.7.5] 337
Solution of a nonlinear equation, exists, rate of convergence      322
Solution of a nonlinear equation, exists, stable      426
Solution of a nonlinear equation, unique      23[1.3.13]
Solution of a nonlinear equation, unique, functional differential equation      393[13.2.3]
Solution of a nonlinear equation, unique, functional equation      352[12.2.2] 362[12.4.1] 364[12.4.2] 387[13.2.1] 393[13.2.4] 396[13.3.1] 399[13.3.2]
Solution of a nonlinear equation, unique, integral equation      317[11.3.1] 319[11.3.2] 324[11.3.4] 332[11.6.2] 333[11.6.3] 356[12.2.6] 364[12.4.3] 384[13.1.1] 385[13.1.2] 392[13.2.2] 401 409[13.5.1] 411[13.5.4] 413[13.5.7] 585[18.6.1]
Solution of a nonlinear equation, unique, integrodifferential equation      328[11.4.3] 334[11.6.4] 336[11.7.4]
Solution of a nonlinear equation, zero at infinity      567[18.2.4] 573[18.3.3] 573[18.3.4] 577[18.4.7] 580[18.4.9] 621[20.3.1] 629[20.4.13] see limit
Spectral, analysis      25[1.3.15]
Spectral, asymptotic spectral subspace      476[15.6.1]
Spectral, radius      239[9.3.18] 260[9.8.6]
Spectral, radius in a Banach algebra      239
Spectral, radius in an associative algebra      239[9.3.17] 290[10.2.10]
Spectral, subspace      472[15.5.1] 472[15.5.2] 473[15.5.3] 474[15.5.6] 475[15.5.7] 475[15.5.8] 485
Spectral, synthesis      463 467[15.4.14] 467[15.4.15] 469[15.4.16] 475[15.5.7] 484[15.10.1] 484[15.10.2] 486
Spectrum in an associative algebra      239[9.3.17] 290[10.2.10]
Spectrum of a bounded function      25[1.3.15] 462[15.4.4] 462[15.4.5] 484[15.10.1] 484[15.10.2]
Spectrum of a constant      469[15.4.17]
Spectrum of a derivative      471 [15.4.18]
Spectrum of a finite measure      25[1.3.15] 461[15.4.1] 461[15.4.2] 462[15.4.3]
Spectrum of a periodic function      470[15.4.17]
Spectrum of a product      465[15.4.10]
Spectrum of a trigonometric polynomial      469[15.4.17] 476[15.6.2]
Spectrum of an almost-periodic function      470[15.4.17] 471
Spectrum of an asymptotically drifting periodic function      476[15.6.2]
Spectrum of an infinitesimal generator      213[8.2.7] 219
Spectrum of an integral operator      260[9.8.6] 275[9.11.2] 276 622—623 623[20.4.1]
Spectrum of an operator      212
Spectrum of the resolvent      260[9.8.6]
Spectrum, asymptotic      476[15.6.1] 476[15.6.2] 548[17.3.7]
Spectrum, asymptotic directional      476[15.6.1]
Spectrum, boundary of the spectrum      467[15.4.13] 467[15.4.14]
Spectrum, continuous dependence      465[15.4.9]
Spectrum, countable      25[1.3.15] 467[15.4.14] 469[15.4.17] 475[15.5.7] 476[15.6.2]
Spectrum, directional      472[15.5.1] 473[15.5.3]
Spectrum, isolated point of the spectrum      466[15.4.12] 469[15.4.17] 474[15.5.6] 476[15.6.2]
Spectrum, nonempty      464[15.4.7] 476[15.6.2]
Spectrum, perfect set      467[15.4.13]
Spectrum, properties of spectra      463[15.4.6] 465[15.4.9] 465[15.4.11] 473[15.5.3] 476[15.6.3]
Spectrum, weak      486
Spectrum, Wiener      487 488
Stability      426
Stability, asymptotic      426
Stability, uniform      330
Stability, uniform asymptotic      330
Stephanov      65
Stieltjes transform      145 150
Strict positive type      see "Kernel strict
Strictly negative matrix      see "Matrix strictly
Strictly positive matrix      see "Matrix strictly
Strong positive type      see "Kernel strong
Submultiplicative function      118[4.3.2] 120[4.4.1] see submultiplicative"
Submultiplicative function, successive approximations      36
Superfluidity      9 [1.2.6]
Support      see "Distribution support" support"
Tauberian decomposition lemma      481 [15.9.1] 482[15.9.2]
Tempered distribution      see "Distribution tempered"
Time independent      see "Autonomous"
Total variation of a function      92[3.5.1]
Total variation of a measure      92[3.5.2] 94[3.5.7]
Total variation, totally bounded set      40 40[2.2.5] 346
Total variation, totally invariant type      see "Kernel C-totally
Totally positive type      see "Kernel totally
Transform conditions, summary      29[1.3.18] 563—564
translate      63[2.7.1] 316 453[15.2.2] 492
Translate, properties      63[2.7.2] 63[2.7.3]
Translation, group      215
Translation, invariant set      453 453[15.2.3] 454[15.2.5] 459[15.3.6] see autonomous"
Trigonometric polynomial      469[15.4.17] 476[15.6.2}
True adjoint      221
TYPE      see "Kernel type"
Uniform convergence on compact subsets      315[11.2.3] 453[15.2.3] see
Uniqueness      see "Differential resolvent unique" "Resolvent unique" "Solution unique"
Unstable      195 197 see
Uryson operator      345
Variation of constants formula      see "Solution of a linear equation variation
Variational equation      397 401
Viscoelasticity      10 [1.2.7]
Volterra, abstract Volterra operator      379 see
Volterra, equation of mixed kind      12[1.2.8]
Volterra, equation of the first kind      4 17[1.3.5] 140 156
Volterra, equation of the second kind      2 3 14[1.3.2] 225
Volterra, integrodifferential equation      15[1.3.3] 76
Volterra, kernel      14[1.3.2] 15[1.3.3] 16[1.3.4] 227[9.2.1]
Volterra, measure kernel      20 [1.3.10]
Volterra, nonconvolution equation      3 19[1.3.9] 225
Volterra, nonconvolution measure kernel      284[10.2.1]
Volterra, nonseparable equation      30[1.3.20] 638
Volterra, resolvent      232[9.3.1]
Weakly compact      254
Weight function      16[1.3.4] 115[4.2.1] 192—200 315
Weight function, dominated by a submultiplicative function      118[4.3.2] 119[4.3.3] 119[4.3.5] 133[4.5.1]
Weight function, properties      117[4.3.1]
Weight function, regular      118[4.3.2] 215[8.3.1] 216[8.3.5]
Weight function, submultiplicative      119[4.3.4] 119 120[4.4.1] 121[4.4.2] 125[4.4.3] 125[4.4.4] 127[4.4.7] 130[4.4.13] 130[4.4.14] 130[4.4.15] 322[11.3.3]
Weighted space, function space      16[1.3.4] 115 522 526
Weighted space, measure space      16[1.3.4] 119
Wiener spectrum      487 488
Wiener's Tauberian theorem      464[15.4.7] 477[15.6.4] 547

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