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Grenander U. — Toeplitz Forms and Their Applications
Grenander U. — Toeplitz Forms and Their Applications

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Название: Toeplitz Forms and Their Applications

Автор: Grenander U.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd

Год издания: 1984

Количество страниц: 245

Добавлена в каталог: 01.03.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\sigma$-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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