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Hinton D., Schaefer P.W. — Spectral Theory and Computational Methods of Sturm-Liouville Problems
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Название: Spectral Theory and Computational Methods of Sturm-Liouville ProblemsАвторы: Hinton D., Schaefer P.W. Аннотация: Presenting the proceedings of a recent conference on Sturm-Liouville problems held in conjunction with the 26th Barrett Memorial Lecture Series at the University of Tennessee, Knoxville, this timely volume covers both qualitative and computational theory of Sturm-Liouville problems - surveying current questions in the field as well as describing novel applications and concepts. Spectral Theory and Computational Methods of Sturm-Liouville Problems reviews boundary value problems for ordinary differential equations...details the dependence of eigenvalues on parameters of the problem, such as interval endpoints, boundary conditions, and coefficients of the equation...addresses the question of approximating singular problems by regular ones...proposes accurate approaches to software computation of eigenfunctions from a small set of values...discusses methods for eigenvalue computation of bounds and enclosures...reconstructs wavespeed in a nonhomogeneous medium from scattering data...furnishes important applications in optical fiber design, chemical photodissociation, and interface conditions...and more. Containing references, drawings, tables, and 1400 display equations, this excellent self-contained resource of active research is indispensable for theoretical and applied mathematicians; computational physicists, numerical analysts, and computer scientists specializing in scientific computing; mechanical engineers; and graduate students in these disciplines.
Язык: Рубрика: Математика /Анализ /Дифференциальные уравнения /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 400Добавлена в каталог: 09.04.2005Операции: Положить на полку |
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Предметный указатель
Absolutely continuous spectrum 100 308 Adjoint systems 23 Airy function approximation 393 Asymptotic averaging 304 Band continuous spectrum 366 Behnke — Goerisch equation 98 Bessel equation 87 172 178 368 BEZ equation 89 Bound state 106 110 114 Boundary conditions, complex coupled 62 Boundary conditions, containing eigenparameter 183 371 Boundary conditions, coupled 48 51 219 Boundary conditions, Friedrichs 355 Boundary conditions, inherited 83 Boundary conditions, interface 212 224 Boundary conditions, interval 100 240 Boundary conditions, periodic 287 Boundary conditions, real coupled 61 Boundary conditions, regular 45 Boundary conditions, semi-periodic 287 Boundary conditions, separated 47 53 61 214 Boundary conditions, singular 73 Boyd equation 88 Characteristic numbers 380 Circle method 199 Coffey — Evans equation 364 Collocation 340 Comparison problem 314 321 Complete orthogonal set 254 256 Continuous dependence, eigenfunctions 57 Continuous dependence, eigenvalues 57 Continuous dependence, solutions 14 30 Continuous extension 28 Contraction mapping 5 Coupling constant 380 Deficiency indices 235 Delta interactions 245 Diagonalization approximate 204 Diagonalization exact 202 Differentiable dependence, eigenvalues 66 Differentiable dependence, solutions 16 32 Dirichlet condition 259 Dirichlet's formula 258 Discontinuous coefficients 107 Discrete spectrum 255 Dunford — Schwartz equation 94 Eigenvalue approximation 85 Eigenvalue bounds 314 Elliptic problems 325 Elliptical coordinates 379 Elliptical core fibers 378 Embedded eigenvalue 290 Enclosure intervals 313 Endpoint classification, limit circle 37 151 121 215 217 231 Endpoint classification, limit circle nonoscillatory 37 28 151 351 354 Endpoint classification, limit circle oscillatory 37 354 Endpoint classification, limit point 37 151 198 215 231 301 354 Endpoint classification, nonoscillatory 37 Endpoint classification, oscillatory 32 Endpoint classification, regular 36 78 215 351 353 Endpoint classification, weakly regular 86 353 Essential spectrum 76 83 150 288 Even and odd modes 378 Existence 3 Exponential map 21 Exponential polynomials 126 Factorization 41 Fourier equation 49 Friedrichs extension 26 Frobenius solution 267 390 Fundamental matrix 8 Generalized eigenvalue problem 136 Generalized solution 188 230 Green's formula 215 228 258 Greens function 338 Gronwall inequality 9 Halvorsen equation 88 Hardy inequality 160 Hardy spaces 116 harmonic oscillator equation 93 HELP inequality 199 207 Herglotz representation 302 Homotopy method 314 321 Hydrogen atom equation 91 364 Indefinite real matrix 136 Indefinite weight function 351 371 Interior singularities 212 Interpolant 336 Inverse eigenvalue problem 135 Inverse scattering problem 105 Jacobi equation 93 Jorgens equation 97 Jost solutions 108 Kato — Rellich theorem 150 Kato's bounds 316 Krall equation 95 L-spline approximates 341 Laguerre, differential expression 252 Laguerre, equation 96 Laguerre, polynomials 253 Laplace tidal wave equation 89 Latzko equation 89 328 Left definite theory 272 Left-definite problem 100 Legendre equation 86 363 Lehmann's method 319 Linear functional 189 Liouville transformation 111 Lohner equation 97 Marchenko integral equation 119 Marietta equation 93 Mathieu equation 90 357 380 381 Matrix of moments 137 Maximal domain 38 229 258 353 Maximal operator 74 150 229 Meissner equation 96 Minimal operator 74 150 Morse oscillator equation 94 NAG code SL02F 285 333 349 Nevanlinna function 198 Nonhomogeneous medium 106 108 normalization constant 137 Operator pencils 181 Operator, compact 189 Operator, left-definite 255 Operator, right-definite 255 Perturbation 149 288 Photodissociation 388 390 Plum equation 90 Positive definite, inner product 255 Positive definite, matrix 136 Positive definite, operator 191 Positive definite, sequence 140 Potential, long range 308 Potential, Morse 344 Potential, periodic 287 310 Potential, repulsive 390 Potential, short range 308 Potential, sparse 310 Principal solution 72 Principal submatrices 143 probability density 308 Propagation constant 378 388 Rayleigh — Ritz method 194 314 317 Reduced scattering coefficients 109 Reduced scattering matrix 110 Reflection coefficient 106 108 125 Refractive index 379 Regularizing functions 39 181 Relatively bounded 149 Relatively compact 150 Residual correction 339 Resolvent set 288 Richardson extrapolation 335 Riemann — Hilbert problem 107 114 116 Riesz basis 186 Riesz representation theorem 189 Right-definite theory 258 Scattering coefficients 107 108 Scattering data 124 Schrodinger equation 301 388 Sears — Titchmarsh equation 88 Singular spectrum 308 SLDRIVER 349 374 SLEDGE 175 285 333 349 SLEIGN 175 285 333 349 SLEIGN2 76 86 175 182 285 330 349 SLTSTPAK 350 Sobolev space 256 Spectral density function 302 305 Spectral function 136 137 198 208 286 Spectral measure 302 STANDARD problem set 352 Stieltjes inversion formula 198 Strong limit point 259 Successive approximations 5 Three term recurrence 135 Titchmarsh — Weyl function 198 232 302 377 Titchmarsh — Weyl matrix 204 Transmission coefficient 107 108 Tridiagonal matrix 136 Uniform convergence 292 Uniqueness 3 27 Unitary transformation 151 278 Variation of parameters 9 Walker method 378 386 Wave equation 106 Weakly guidring modes 385 Weinstein's bounds 315 Weyl circle 199 Weyl dichotomy 231 Whittaker equation 98 WKB solution 392
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