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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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43 66 43 43 43 30 62 146 18 58 79 117 60 33 183 205 174 181 182 194 197 208 58 60 9 57 9 138 159 203 203 204 204 204 204 170 193 203 21 192 12 14 21 169 95 8 118 88 42 343 18 18 A*, adjoint of A 19 43 Adjoint operator A* 41 Adjoint, boundary condition 83 Annihilator 80 83 103 Annihilator, boundary condition 247 Atkinson, F.V. xiii Atkinson’s theory for singular Hamiltonian systems of even dimension 73 Bavinck 343 Bernoulli numbers 229 Bessel functions 148 153 Bessel operator 331 332 Bessel polynomial equation 239 Bessel's inequality 14 boundary conditions 333 334 336 337 Boundary conditions of linear Hamiltonian systems 343 Boundary conditions, adjoint 83 Boundary conditions, annihilator 247 Boundary conditions, extension of the 122 Boundary conditions, other 102 Boundary conditions, parametric 63 83 130 Boundary conditions, singular 79 117 Boundary form 80 Boundary value problems 97 Boundary value problems, generalized Laguerre 152 Boundary value problems, Hermite 152 Boundary value problems, Jacobi 149 Boundary value problems, Legendre 150 Boundary value problems, Legendre polynomial 134 Boundary value problems, ordinary Laguerre 152 Boundary value problems, regular second order Sobolev 302 Boundary value problems, regular Sobolev boundary value problems for linear Hamiltonian systems 307 Boundary value problems, self-adjoint boundary value problems with mixed boundary conditions 131 Boundary value problems, singular second order Sobolev 330 Boundary value problems, singular Sturm — Liouville xiii Boundary values 142 Bounded linear operator 17 Bounded linear operator on a Hilbert space 17 Bounded monotonic sequence 29 Bounded operator 17 Brown, Dick xiii Cauchy sequence 6 9 10 Cauchy sequence, closed 17 Cayley transform of A 47 Compact set 26 Compact support 207 Compatibility condition 262 Complete orthogonal set 248 Complete orthonormal set 25 Complex linear space 1 Continuous spectrum 25 Convergence, operator 28 Convergence, strong 28 Convergence, uniform 28 Convergence, weak 28 D 61 142 146 Difference equation, second order 343 Differential equation of the second Littlejohn polynomials 289 Differential equation, distributional 215 Differential equation, Legendre 133 Differential equation, self-adjoint differential equation of first order 51 Differential equation, self-adjoint differential equation of fourth order 53 Differential equation, self-adjoint differential equation of second order 52 Differential equation, self-adjoint differential equation of third order 52 Differential equation, self-adjoint, real self-adjoint differential equation of sixth order 54 Differential expression 336 Differential operator 334 336 343 Differential operator L 118 Differential operator, Jacobi 149 Differential operator, self-adjoint 118 Dirac distribution 209 Dirac systems 51 54 Dirichlet formula 305 306 312 315 323 328—337 340 341 Dirichlet formula of the Legendre cubed operator 341 Dirichlet formula of the Legendre squared operator 341 distribution 207 Distribution, Dirac 209 Distribution, Heaviside 209 Distribution, limits of distributions 211 Distribution, of compact support, E' 214 Distribution, of rapid decay, P'$ 213 Distribution, of rapid growth 208 Distribution, of slow growth, S' 212 Distribution, Schwarz xiii Distribution, without constraint, D' 207 Distributional differential equations 215 Distributional weight function 261 275 Domain of A*, 43 e(A) 33 Eigenfunction 66 Eigenfunction, expansion xiii Eigenvalues of 91 Even Hermite operator 254 Everitt, W.N. xiii Extended Green’s formula with two singular points 145 Extension of the boundary conditions 122 F(X) 182 Fourier cosine transform 331 Fourier sine transform 185 331 Fourier transform 213 330 Fulton, Charles xiii Function, 138 Function, Bessel 148 Function, distributional weight 261 Function, Riemann integrable 2 Function, support of a 207 Function, T, class of all piecewise continuous functions on [m, M] 32 Function, test function of rapid decay, S 212 Function, test function of slow growth, P 213 Function, test function with compact support, D 207 Function, test function without constraint, E 214 Function, weight 281 Gegenbauer operator 264 Generalized even Hermite operator 336 Generalized Hermite polynomials 252 Generalized Hermite polynomials form a complete orthogonal set 256 Generalized Hermite polynomials of even degree 253 Generalized Hermite polynomials of odd degree 255 Generalized Jacobi-type polynomials 291 292 Generalized Koekoek’s — Jacobi-type polynomials 290 Generalized Laguerre boundary value problem 152 Generalized Laguerre equation 238 Generalized Laguerre operator 334 Generalized Laguerre polynomials 148 245 264 Generalized Laguerre-type polynomials 295 296 Generalized odd degree Laguerre — Hermite polynomials 337 Generalized odd Hermite operator 256 336 Gram — Schmidt Theorem 13 Graph of A* in 43 Graph of A, 42 Green’s formula 129 146 272 Green’s formula, extended Green’s formula with one singular point 125 Green’s formula, extended Green’s formula with two singular points 145 H.L. Krall polynomials 281 Hamiltonian systems, Atkinson’s theory for singular Hamiltonian systems of even dimension 73 Hamiltonian systems, boundary conditions of linear 343 Hamiltonian systems, left definite singular 343 Hamiltonian systems, Niessen approach to singular 87 Hamiltonian systems, regular 328 Hankel transform 332 333 Hazmirzaahmad, Mojdeh xiv Heaviside distribution 209 Hermite boundary value problem 152 Hermite equation 239 Hermite operator 336 Hermite operator, even 254 Hermite operator, generalized even 336 Hermite operator, generalized odd 256 336 Hermite polynomial 336 Hermite polynomial problems 133 Hermite polynomial, odd degree generalized 337 Hermite polynomials 148 249 265 Hermite polynomials form a complete orthogonal set 251 Hermite polynomials generalized 252 Hermite polynomials, generalized Hermite polynomials form a complete orthogonal set 256 Hermite polynomials, generalized Hermite polynomials of even degree 253 Hermite polynomials, generalized Hermite polynomials of odd degree 255 Hermite polynomials, series representation of the 250 Hermitian form 3—5 Hermitian form, positive definite 6 Hilbert space xiii 6 343 Hilbert, isometric 15 Hinton and Shaw’s extension of Weyl’s 107 Hinton and Shaw’s extension with two singular points 137 Hinton, Don xiii Identity operator, I 18 Identity, polarization 7 Inequality, Bessel’s 14 Inequality, Minkowski’s 6 7 Inequality, Schwarz’s 6 7 Inner product space 9 10 Integral, Lebesgue 3 8 Integral, Lebesgue — Stieltjes 9 Integral, Riemann 8 Isometric Hilbert space 15 Jacobi boundary value problem 149 Jacobi differential operator 149 Jacobi equation 238 Jacobi operator 334 Jacobi operator, spectral resolution of the 334 Jacobi polynomials 148 239 263 Jacobi polynomials, series representations of the 240 Jacobi-type operator 274 341 Jacobi-type polynomials 274 Jacobi-type polynomials, generalized 291 292 Jacobi-type polynomials, Koekoek’s generalized 290 Jacobi-type problems of fourth order 343 Jirari, Alouf xiv Kaper, Hans xiii Koekoek 343 Koekoek’s generalized Jacobi-type polynomials 290 Krall, H.L.(1907—1994) xiv Krein space 259 L 64 L* 64 147 L, self-adjoint 121 Laguerre equation, generalized 238 Laguerre operator, generalized 334 Laguerre polynomials 335 Laguerre polynomials, generalized 148 245 264 Laguerre polynomials, series representation of the 246 Laguerre-type operator 270 340 Laguerre-type polynomials 270 340 Laguerre-type polynomials in a Sobolev space 339 Laguerre-type polynomials, generalized 295 296 Laguerre-type problem 155 Laplacian operators 330 Lebesgue integral 3 8 Lebesgue — Stieltjes integral 9 Lebesgue — Stieltjes measure 8 Left-definite theory 302 Legendre boundary value problem 150 Legendre differential equation 133 Legendre differential expression 333 Legendre operator 264 Legendre operator, cubed 341 Legendre operator, higher powers of the 341 Legendre operator, spectral resolution of the 334 Legendre operator, squared 341 Legendre polynomial boundary value problem 134 Legendre polynomials 243 Legendre squared problem 154 Legendre-type operator 266 268 Legendre-type polynomials 265 Legendre-type polynomials in a Sobolev space 339 Lemma, Riemann — Lebesgue 14 Limit circle case 317 Limit point case 316 Linear Hamiltonian system xiii Linear manifold 2 10 Linear operators 343 Linear space 1 Littlejohn operator 288 Littlejohn polynomials 287 Littlejohn polynomials, second 289 Littlejohn, Lance xiii Ly 142 146 M-circle 111 Manifold, linear 2 10 Measure, Lebesgue — Stieltjes 8 Mingarelli, Angelo xiii Minkowski’s inequality 6 7 Mixing operators, U, V 42 Moment equations 244 263 266 271 275 283 Moment relations 263 264 Moments 223 226 249 264 283 Niessen approach to singular Hamiltonian systems 87 Niessen, Heinz — Dieter xiii normal 19 Operator 45 Operator 45 Operator bounded 17 Operator convergence 28 Operator convergence, strong 28 Operator convergence, uniform 28 Operator convergence, weak 28 Operator, adjoint operator of A* 41 Operator, bounded linear 17 Operator, bounded linear operator on a Hilbert space 17 Operator, Gegenbauer 264 Operator, I, identity 18 Operator, Laplacian 330 Operator, Legendre 264
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