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Catalogue Information
Field name	Details
Dewey Class	515
Title	Monotone Matrix Functions and Analytic Continuation ([EBook]) / by William F. Donoghue.
Author	Donoghue, William F. , 1921-2002
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1974.
Physical Details	X, 184 pages : online resource.
Series	Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 0072-7830 ; ; 207
ISBN	9783642657559
Summary 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.:
Contents 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-65755-9
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Donoghue, William F. 1921-2002 . Donoghue, William F., 1921-2002. . Corporate Authors: SpringerLink (Online service) . Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete . Classification: 515 .

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Monotone Matrix Functions and Analytic Continuation

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