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Krall A.M. — Hilbert Space, Boundary Value Problems, and Orthogonal Polynomials
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Название: Hilbert Space, Boundary Value Problems, and Orthogonal PolynomialsАвтор: Krall A.M. Аннотация: Many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. While function theory has often been employed to answer algebraic questions such as the existence of idempotents in a Banach algebra, concepts arising from the study of Banach algebras including the maximal ideal space, the Silov boundary, and Gleason parts, have led to new questions and to new methods of proofs in function theory. This book is concerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader, and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. The third edition of this book contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter containing commentaries on history and recent developments and an updated and expanded list of references.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2002Количество страниц: 353Добавлена в каталог: 13.12.2009Операции: Положить на полку |
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Предметный указатель
Operator, Littlejohn 288 Operator, mixing operators, U, V 42 Operator, norm of A, ||A|| 18 Operator, P, projection 21 Operator, polynomial 23 Operator, projection 69 Operator, resolvent 18 Operator, self-adjoint xiii 17 Operator, Tchebycheff 264 Operator, unbounded linear 41 Ordinary Laguerre boundary value problem 152 Orthogonal 7 Orthogonal polynomials xiii 223 343 Orthogonal polynomials satisfying fourth order differential equations 261 Orthogonal polynomials satisfying higher order differential equations 291 Orthogonal polynomials satisfying second order differential equations 237 Orthogonal polynomials satisfying sixth order differential equations 281 Orthogonal polynomials, basic properties of 223 Orthogonality 6 Orthonormal set 7 13 Other boundary conditions 102 P = P* 21 P and Q 61 Parallelogram law 6 7 9 Parametric boundary conditions 63 83 130 Parseval’s equality 15 169 192 Point spectrum 25 Polarization 5 Polarization identity 7 Polynomial operator 23 Polynomials, generalized Laguerre 148 Polynomials, Hermite 148 Polynomials, Jacobi 148 Polynomials, orthogonal xiii 223 343 Polynomials, Tchenbycheff 223 Pontrjagin space 240 Positive definite Hermitian form 6 Projection 21 Projection operator, P 21 69 Projection valued measure, 243 252 Pythagorean Theorem 7 22 Regular linear Hamiltonian systems 51 Regular second order Sobolev boundary value problems 302 Relativistic quantum mechanics 55 Residual spectrum 25 27 Resolution, spectral 69 Resolution, spectral resolution of a bounded self-adjoint operator 33 Resolution, spectral resolution of an unbounded self-adjoint operator 46 Resolution, spectral resolution of bounded normal and unitary operators 37 Resolution, spectral resolution of bounded normal operators 37 Resolution, spectral resolution of unitary operators 39 Resolvent of A, 18 Resolvent of L 121 Resolvent operator 18 Riemann integrable function 2 Riemann integral 8 Riemann — Lebesgue lemma 14 Riesz — Fischer theorem 14 Riesz — Frechet theorem 12 s(A) 32 S-Hermitian systems 51 56 Schwarz distribution xiii Schwarz’s inequality 6 7 Second order difference equation 343 Self-adjoint 19 20 45 144 333—335 337 339 340 Self-adjoint boundary value problems with mixed boundary conditions 131 Self-adjoint differential equation of first order 51 Self-adjoint differential equation of fourth order 53 Self-adjoint differential equation of second order 52 Self-adjoint differential equation of third order 52 Self-adjoint differential operator 118 336 Self-adjoint operator xiii 17 Self-adjoint real, differential equation of sixth order 54 Self-adjoint, L is 121 Sequence bounded monotonic 29 Sequence, Cauchy 6 9 10 Sequence, closed Cauchy 17 Series representations of the Hermite polynomials 250 Series representations of the Jacobi polynomials 240 Series representations of the Laguerre polynomials 246 Set of ordered pairs {x,y}, 42 Set orthonormal 7 13 Set, compact 26 Set, complete orthogonal 248 Set, complete orthonormal 25 Shaw, Hinton and Shaw’s extension of Weyl’s 107 Shaw, Hinton and Shaw’s extension with two singular points 137 Shaw, Ken xiii Singular boundary conditions 79 117 Singular point 74 Singular Sturm — Liouville boundary value problems xiii Sixth order differential equations 287 Sixth order differential operator 282 Sobolev boundary value problems, regular Sobolev boundary value problems for linear Hamiltonian systems 307 Sobolev boundary value problems, singular second order 330 Sobolev inner product 303 305 Sobolev space 295 298 302 305 308 327 336 340 341 Sobolev space, Laguerre-type polynomials, in a 339 Sobolev space, Legendre-type polynomials, in a 339 Solutions, square inegrable 115 Space, 343 Space, complex linear 1 Space, Hilbert xiii 6 343 Space, inner product 9 10 Space, isometric Hilbert 15 Space, Krein 259 Space, linear 1 Space, Pontrjagin 240 Space, Sobolev 295 298 302 305 308 327 336 340 341 Spectral expansion 168 Spectral resolution 69 335—337 Spectral resolution for linear Hamiltonian systems with one singular point 167 Spectral resolution for linear Hamiltonian systems with two singular points 189 Spectral resolution of a bounded self-adjoint operator 33 Spectral resolution of an unbounded self-adjoint operator 46 Spectral resolution of bounded normal and unitary operators 37 Spectral resolution of the Jacobi operator 334 Spectral resolution of the Legendre operator 334 Spectrum 333 Spectrum of A, 18 Spectrum, continuous spectrum, 25 Spectrum, point spectrum, 25 Spectrum, residual spectrum 25 27 Square integrable solutions 115 Stieltjes measure 70 Stirling number of the second kind 342 Stirling numbers 342 subspace 2 Subspace expansions 185 Support compact 207 Support of a function 207 symmetric 45 Symmetry factor 226 232 System, Dirac 51 54 System, linear Hamiltonian xiii System, regular linear Hamiltonian 51 System, S-Hermitian 51 56 T(A) 33 T, class of all piecewise continuous functions on [m,M] 32 Tchebycheff operator 264 Tchebycheff polynomials 223 261 Tchebycheff problem of the first kind 150 Tchebycheff problem of the second kind 151 Tchebycheff test function of rapid decay, S 212 Tchebycheff test function of slow growth, P 213 Tchebycheff test function with compact support, D 207 Tchebycheff test function without constraint, E 214 Theorem, Gram — Schmidt 13 Theorem, Pythagorean 7 22 Theorem, Riesz — Fischer 14 Theorem, Riesz — Frechet 12 Three term recurrence relation 225 238 244 247 250 262 267 271 276 282 287 297 Unbounded linear operator 41 Unitary 19 Weight equation 244 246 250 263 264 Weight function 281 Weight function, distributional 261 Weight functional 223 Weight problem 257 Weyl circle 165 Weyl — Titchmarsh limit point-limit circle theory 315 Zettl, Tony xiii ||A||, operator norm of A 18
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