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| Grenander U. — Toeplitz Forms and Their Applications |
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| Предметный указатель |
Abelian group 167
Absolutely continuous function 6
Analytic curve 29
Approximations 14
Barriers 201
Bessel functions 139
Best linear estimate 209
Best predictor 181
Borel field 34
Canonical distribution 109
Cauchy sequence 167
Cauchy's principal value 27
Characteristic function 170
Charlier polynomials 134
Christoffel numbers 115
Circulant (cyclic) matrices 112
Class (space) 4—5
Commutative matrices 105
Completeness 11
Conformal mapping 30
Consistent estimates 205
Continuity in the mean 167
Continuous stationary process 193
Convex function 20
Covariance, function 166
Covariance, matrix 168
Crystal 232
Cumulants 220
Deterministic process 176
Distribution of eigenvalues 63
Distribution of eigenvectors 107
Distribution of quadratic forms 217
Distribution, canonical 109
Distribution, function 4
Eigenvalues of Hermitian forms 32
Eigenvalues of Toeplitz forms 62
Eigenvalues, distribution 63
Eigenvalues, examples 66
Eigenvalues, extreme 72
Eigenvalues, Sturm — Liouville problem 117
Eigenvectors 107
Elementary events 164
Equal distribution 62
Expected value 192
Extreme eigenvalues 72
Faber polynomials 29
Fejer kernel 210
Fourier series 12
Fourier — Plancherel transform 102
Fourier — Stieltjes, coefficients 19
Fourier — Stieltjes, integral 168
Fourier's inversion formula 214
Frequency response 187
Functional 9
Gain 187
Gauss — Jacobi formula 114
Generating functions of Toeplitz matrices 128
Geometric mean 26
Group of transformations 172
Haar system 119
Hankel forms 82
Hankel transform 139
Hellinger integral 207
Hermite polynomials 132
Hermitian form 3
Hermitian form, associated with a curve 84
Hermitian form, associated with a function of two variables 92
Hilbert space 10
Hilbert — Schmidt kernel 97
Inequality of Cauchy 25
Inequality of Hoelder 5
Inequality of Jensen 24
Inequality of Minkowski 5
Integral equation 139
Integrals 4
Integration by parts 4
Jacobi polynomials 102
Jacobi transformation 163
Jacobi — Jensen's formula 23
Jordan curve 29
Jump function 5
Kernel, function 50
Kernel, orthogonal 99
Kernel, polynomial 39
Kernel, Toeplitz 102
Laplace transform 141
Laurent polynomial 192
Laurent series 62
Legendre polynomials 82
Linear algebra 123
Linear estimation 204
| Linear independence 13
Linear predictor 177
Linear stationary problems 191
Lipschitz condition 15
Lipschitz — Dini condition 15
Matrix 3
Measure,  -finite 34
Measure, probability 164
Measure, product 99
Measure, space 34
Mechanical quadrature 114
Mehler's formula 133
Metric 102
Modulus of continuity 4
Moving Average 183
Nondeterministic process 177
Operator, completely continuous 97
Operator, finite Toeplitz 101
Operator, linear 34
Operator, Toeplitz 101
Optimality criterion 174
Orthogonal (orthonormal) system 12
Orthogonal process 173
Orthogonalization (Gram — Schmidt) 13
Orthonormal polynomials on an interval 89
Orthonormal polynomials on the unit circle 37
Orthonormal polynomials on the unit circle, asymptotic formula 50
Orthonormal polynomials on the unit circle, extremum properties 38
Orthonormal polynomials on the unit circle, zeros, identities 40
Parseval's formula 22
Phase shift 187
Plancherel transform 136
Poisson integral 10
Poisson summation formula 139
Prediction of error 176
Prediction of h units of time ahead 184
Prediction of stationary processes 174
Probability measure 164
Quadratic form 3
Radon — Nikodym derivative 110
Random walk 200
Reciprocal polynomial 3
Refinement of the distribution theorem 75
Representation of nonnegative trigonometric polymials 20
Representation of positive functions 23
Representation, spectral 171
Response 187
Riemann — Lebesgue lemma 190
Selection theorem 6
Set-function 34
Singular function 6
Spectral representation 171
Spectrum of a stationary process 168
Statistical inference 204
Stochastic, process 165
Stochastic, variable 164
Sturm — Liouville eigenvalue problem 117
Tchebychev polynomial 31
Theorems, C. Caralh6odory 56
Theorems, D. Hilbert (resolution of identity) 36
Theorems, F. Riesz and E. Fischer 12
Theorems, H. Cramer 173
Theorems, H. Weyl and R. Courant 32
Theorems, Hardy — Littlewood 130
Theorems, L. Fejer and F. Riesz 20
Theorems, Privalov 79
Theorems, S. Bernstein 29
Theorems, selection 6
Theorems, Stone 172
Theorems, Tauber 131
Theorems, Weierstrass 14
Toeplitz determinants 38
Toeplitz forms (matrices), associated with a distribution function 17
Toeplitz forms (matrices), associated with a harmonic function 17
Toeplitz forms (matrices), associated with a real function 17
Toeplitz forms (matrices), associated with Hermite polynomials 132
Toeplitz forms (matrices), associated with orthogonal polynomials 114
Toeplitz forms (matrices), general 99
Toeplitz forms (matrices), generalizations and analogs 81
Toeplitz forms (matrices), generating functions of 128
Toeplitz forms (matrices), minimum of 44
Toeplitz integral kernels of Bessel type 139
Toeplitz integral kernels of Fourier type 139
Total variation 9
Trace 3
Trace completeness 109
Transfinite diameter 30
Trigonometric moment problem 19
Vector, vector space 10
Watson transform 141
Weight function 11
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