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Donoghue Jr.W.F. — Monotone Matrix Functions and Analytic Continuation
Donoghue Jr.W.F. — Monotone Matrix Functions and Analytic Continuation



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Название: Monotone Matrix Functions and Analytic Continuation

Автор: Donoghue Jr.W.F.

Аннотация:

A Pick function is a function that is analytic in the upper half-plane with positive imaginary part. In the first part of this book we try to give a readable account of this class of functions as well as one of the standard proofs of the spectral theorem based on properties of this class. In the remainder of the book we treat a closely related topic: Loewner's theory of monotone matrix functions and his analytic continuation theorem which guarantees that a real function on an interval of the real axis which is a monotone matrix function of arbitrarily high order is the restriction to that interval of a Pick function. In recent years this theorem has been complemented by the Loewner-FitzGerald theorem, giving necessary and sufficient conditions that the continuation provided
by Loewner's theorem be univalent.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 182

Добавлена в каталог: 05.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute continuity      53
Almost positive matrix      134
Bendat and Sherman      85
Bergman kernel function      92 141
Bernstein, S.N.      13
Big Bernstein theorem      14
Caratheodory, C.      157
Cauchy interpolation problem      100
Choquet, G.      170
Completely monotone function      13
Degree of rational function      1
Differential      79
Divided difference      1
Eberlein, W.      171
entropy      148
Exceptional solution      107
Exponential representation      27
Extended Loewner matrix      40
Fatou theorem      44
Fehrman, J.      173
FitzGerald, C.      140 144 151 167
Gamma function      29
Gram's matrix      8
Hamburger moment problem      85
Harmonic measure      159
Hilbert — Schmidt norm      66 78
Hindmarsh, A.      36
Infinitely divisible      135
Integral representation      20 21
Kernel function      89
Koranyi and Nagy      85 94
Leibnitz rule      6
Linear problem      101
Little Bernstein theorem      13
Local property      82 83 131
Loewner matrix      39
Loewner — FitzGerald theorem      146
Loewner's theorem      85 96 126
Matrix function      67
Monotone matrix function      68
Multiplicity function      58
Newtonian interpolation polynomials      3
One-dimensional perturbations      63
One-dimensional projections      9 63
operator function      67
Pade table      172
Pick function      18
Pick matrix      34
Pick — Nevanlinna interpolation      172
Pick's theorem      94 117
Pick, G.      94
Positive matrix      7 88
Radon — Nikodym derivative      54
Regularization      11
Remainder theorem      7
Reproducing kernel      89
Reproducing kernel space      88 89
Resolvent      51
Resolvent equation      51 53
Robertson, A.      170
Schur exponential      10 93
Schur product      9
Schur, I.      9
Schwarz inequality      8
Seidel, W.      174
Self-adjoint      50
Sesqui-analytic function      92
Spectral theorem      50 62
Univalent      146
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