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Krall A.M. — Hilbert Space, Boundary Value Problems, and Orthogonal Polynomials
Krall A.M. — Hilbert Space, Boundary Value Problems, and Orthogonal Polynomials

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Название: Hilbert Space, Boundary Value Problems, and Orthogonal Polynomials

Автор: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 353

Добавлена в каталог: 13.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(A^{-1})^*$      43
$(L - \lambda I)^{-1}$      66
$A^{**}$      43
$A^{**}$ = A      43
$A^{-1}$      43
$A^{\frac{1}{2}}$      30
$D^*$      62 146
$D^\bot$      18
$d_M$      58 79 117
$D_{L_0^*}$      60
$E(\mu)$      33
$E_\lambda F(x)$      183 205
$g(\Lambda)$      174 181 182 194 197
$H_r$      208
$L^*_0$      58 60
$L_A^2(a,b)$      9 57
$L_p^2(a,b)$      9
$M(\lambda)$ functions      138
$M(\lambda)$ surface      159
$M_a$      203
$M_b$      203
$M_{11}$      204
$M_{12}$      204
$M_{21}$      204
$M_{22}$      204
$p(\lambda)$      170 193 203
$P^2 = P$      21
$P_I(\lambda)$      192
$P_M$, projection of H onto M      12 14 21
$P_{b^{'}}(\lambda)$      169
$\ell Y$      95
$\ell^2$      8
$\lambda_0$ fixed      118
$\mathcal{A}(x)$      88
$\mathcal{H} = H\otimes H$, set of ordered pairs {x,y}      42
$\pi - \kappa$ spaces      343
$\rho(A)$, resolvent of A      18
$\sigma(A)$, spectrum of A      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 $\{B_{2r}\}_{r=1}^\infty$      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 $\sigma_c(A)$      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*, $D^*$      43
e(A)      33
Eigenfunction      66
Eigenfunction, expansion      xiii
Eigenvalues of $\mathcal{A}(x,\lambda)$      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, $M(\lambda)$      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 $\mathcal{H}$, $G_A^*$      43
Graph of A, $G_A$      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 $M(\lambda)$ theory to systems      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 $B = (I + A^{*}A)^{-1}$      45
Operator $C = A(I + A^{*}A)^{-1}$      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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