0387986995Basic TheoryC

468

INDEX

Stegun, 1. A., 141, 449, 450

Sternberg, W., 403, 438

Stirling formula, 358, 364 Sturm-Liouville problem, 148 Subalgebra, 109

Successive approximations, 3, 20, 21, 378,

418

Sufficient condition, for asymptotic stability, 241

for uniqueness, 61, 63 for unstability, 243

Summability of a formal power series,

371, 442, 443

Symplectic group Sp(2n, R), 92, 93 matrix of order 2n, 92, 93 107

Tahara, H., 112

Tanaka, S., 144 Taylor's series, 345

Transform, incomplete Leroy, 354

Transformation, shearing, 209 Transversal, to orbit, 291, 292 with respect to a vector, 291

Trivial solution, 236, 243

Turrittin, H. L., 391, 403, 428 Turrittin, Hukuhara-, theorem, 428

Two dimensional system with constant coefficients, 251

Unbounded operators, 103

Uniformly asymptotic series, 343, 357,

361

Uniqueness, Lipschitz condition, 1, 3, 64 Nagumo condition, 64, 65

of S-N decomposition of a matrix, 75 of asymptotic expansion, 343

of formal solution, 115

of solution of a boundary-value problem, 150

of solution of an initial-value problem, 1, 3, 21, 79 Osgood condition, 63, 65

sufficient conditions for, 61, 63 Unstable manifold, 246

Upper-triangular matrix, 70

Urabe, M., 288

Uvarov, V. Q., 141

V image of P, (A), 73 direct sum for C", 73

van der Pol equation, 312 for a large parameter, 322 for a small parameter, 319

singular perturbation of, 330

Variation of parameters, formula of, 101 Vector, infinite-dimensional, 120, 393

norm of, 393

Vector space of solutions, 78

Wasow, W., 108, 304, 342, 372, 382, 449

Watson, G. N., 141, 342, 359

Weinberg, L., 142, 447

Weyl, H., 69

Whittaker, E. T., 141

Winkler, S., 196

Wintner, A., 197

Wronskian, 145, 149, 168, 172

Xie, F., 197, 217 x"C{x}", 110

x"C((Fx)l", 110

Yoshida, M., 138

Zeros, of eigenfunctions, 185 of solutions, 144

Zygmund, A., 167

468

Universitext

(continued )

Moise: Introductory Problems Course in Analysis and Topology

Morris: Introduction to Game Theory Polster: A Geometrical Picture Book

Porter/Woods: Extensions and Absolutes of Hausdorff Spaces

Ramsay/Rlchtmyer: Introduction to Hyperbolic Geometry

Reisel: Elementary Theory of Metric Spaces

Rickart: Natural Function Algebras Rotman: Galois Theory

Rubel/Colliander: Entire and Meromorphic Functions

Sagan: Space-Filling Curses Samelson: Notes on Lie Algebras

Schif: Normal Families

Shapiro: Composition Operators and Classical Function Theory Simonnet: Measures and Prohabilit

Smith: Power Senes From a Computational Point of View Smorytiski: Self-Reference and Modal Logic

Stillwell: Geometry of Surfaces

Stroock: An Introduction to the Theory of Large Deviations Sunder: An Invitation to von Neumann Algebras

Tondeur: Foliations on Riemannian Manifolds Wong: Wcyl Transforms

Zhang: Matrix Theory Basic Results and Techniques

Zong: Strange Phenomena in Convex and Discrete Geometry Zong: Sphere Packing-,