عنوان

Monotone matrix functions and analytic continuation

(Number (ISBN

3540065431

(Number (ISBN

3642657559

(Number (ISBN

9783540065432

(Number (ISBN

9783642657559

Number

b572166

Title Proper

Monotone matrix functions and analytic continuation

General Material Designation

[Book]

First Statement of Responsibility

[by] William F. Donoghue.

Place of Publication, Distribution, etc.

Berlin

Name of Publisher, Distributor, etc.

New York, Springer

Date of Publication, Distribution, etc.

1974

Specific Material Designation and Extent of Item

(182 pages)

Series Title

Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebeite, Bd. 207.

Text of Note

I. Preliminaries --; II. Pick Functions --; III. Pick Matrices and Loewner Determinants --; IV. Fatou Theorems --; V. The Spectral Theorem --; VI. One-Dimensional Perturbations --; VII. Monotone Matrix Functions --; VIII. Sufficient Conditions --; IX. Loewner's Theorem --; X. Reproducing Kernels --; XI. Nagy-Koranyi Proof of Loewner's Theorem --; XII. The Cauchy Interpolation Problem --; XIII. Interpolation by Pick Functions --; XIV. The Interpolation of Monotone Matrix Functions --; XV. Almost Positive Matrices --; XVI. The Analytic Continuation of Bergman Kernels --; XVII. The Loewner-FitzGerald Theorem --; XVIII. Loewner's Differential Equation --; XIX. More Analytic Continuation --; Notes and Comment.

Text of Note

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. In order that our presentation should be as complete and trans parent as possible, we have adjoined short chapters containing the in formation about reproducing kernels, almost positive matrices and certain classes of conformal mappings needed for our proofs.

Analytic continuation.

Analytic functions.

Monotonic functions.

[by] William F. Donoghue.

William F Donoghue

Electronic name

[Book]

Y