skip to content
Monotone matrix functions and analytic continuation Preview this item
ClosePreview this item
Checking...

Monotone matrix functions and analytic continuation

Author: William F Donoghue
Publisher: Berlin, New York, Springer, 1974.
Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebeite, Bd. 207.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Donoghue, William F. (William Francis), 1921-2002.
Monotone matrix functions and analytic continuation.
Berlin, New York, Springer, 1974
(DLC) 73015293
(OCoLC)1041036
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: William F Donoghue
ISBN: 9783642657559 3642657559 9783540065432 3540065431
OCLC Number: 707452387
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL
Description: 1 online resource (182 pages).
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: 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.
Series Title: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebeite, Bd. 207.
Responsibility: [by] William F. Donoghue.

Abstract:

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  Read more...

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/707452387> # Monotone matrix functions and analytic continuation
    a schema:CreativeWork, schema:Book, schema:MediaObject ;
    library:oclcnum "707452387" ;
    library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/376226910#Place/berlin> ; # Berlin
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/gw> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/matrixfuncties> ; # Matrixfuncties
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/mathematics> ; # Mathematics
    schema:about <http://id.worldcat.org/fast/808336> ; # Analytic functions
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/analytische_functies> ; # Analytische functies
    schema:about <http://dewey.info/class/515.9/> ;
    schema:about <http://id.worldcat.org/fast/1025723> ; # Monotonic functions
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/physical_sciences_&_mathematics> ; # Physical Sciences & Mathematics
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/matrices> ; # Matrices
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/fonctions_continues> ; # Fonctions continues
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/matrixfunktion> ; # Matrixfunktion
    schema:about <http://id.worldcat.org/fast/808335> ; # Analytic continuation
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/mathematical_theory> ; # Mathematical Theory
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/fonctions_analytiques> ; # Fonctions analytiques
    schema:about <http://experiment.worldcat.org/entity/work/data/376226910#Topic/analytische_fortsetzung> ; # Analytische Fortsetzung
    schema:bookFormat schema:EBook ;
    schema:creator <http://viaf.org/viaf/108132767> ; # William Francis Donoghue
    schema:datePublished "1974" ;
    schema:description "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."@en ;
    schema:description "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."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/376226910> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/376226910#Series/die_grundlehren_der_mathematischen_wissenschaften_in_einzeldarstellungen_mit_besonderer_berucksichtigung_der_anwendungsgebeite> ; # Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebeite ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/1041036> ;
    schema:name "Monotone matrix functions and analytic continuation"@en ;
    schema:productID "707452387" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/707452387#PublicationEvent/berlin_new_york_springer_1974> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/376226910#Agent/springer> ; # Springer
    schema:url <https://link.springer.com/openurl?genre=book&isbn=978-3-540-06543-2> ;
    schema:url <http://catalog.hathitrust.org/api/volumes/oclc/1041036.html> ;
    schema:url <https://0-link-springer-com.pugwash.lib.warwick.ac.uk/10.1007/978-3-642-65755-9> ;
    schema:url <http://public.eblib.com/choice/publicfullrecord.aspx?p=3089803> ;
    schema:url <http://dx.doi.org/10.1007/978-3-642-65755-9> ;
    schema:workExample <http://worldcat.org/isbn/9783642657559> ;
    schema:workExample <http://worldcat.org/isbn/9783540065432> ;
    schema:workExample <http://dx.doi.org/10.1007/978-3-642-65755-9> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/707452387> ;
    .


Related Entities

<http://dbpedia.org/resource/New_York_City> # New York
    a schema:Place ;
    schema:name "New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/376226910#Series/die_grundlehren_der_mathematischen_wissenschaften_in_einzeldarstellungen_mit_besonderer_berucksichtigung_der_anwendungsgebeite> # Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebeite ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/707452387> ; # Monotone matrix functions and analytic continuation
    schema:name "Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebeite ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/376226910#Topic/analytische_fortsetzung> # Analytische Fortsetzung
    a schema:Intangible ;
    schema:name "Analytische Fortsetzung"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/376226910#Topic/analytische_functies> # Analytische functies
    a schema:Intangible ;
    schema:name "Analytische functies"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/376226910#Topic/fonctions_analytiques> # Fonctions analytiques
    a schema:Intangible ;
    schema:name "Fonctions analytiques"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/376226910#Topic/fonctions_continues> # Fonctions continues
    a schema:Intangible ;
    schema:name "Fonctions continues"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/376226910#Topic/mathematical_theory> # Mathematical Theory
    a schema:Intangible ;
    schema:name "Mathematical Theory"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/376226910#Topic/physical_sciences_&_mathematics> # Physical Sciences & Mathematics
    a schema:Intangible ;
    schema:name "Physical Sciences & Mathematics"@en ;
    .

<http://id.worldcat.org/fast/1025723> # Monotonic functions
    a schema:Intangible ;
    schema:name "Monotonic functions"@en ;
    .

<http://id.worldcat.org/fast/808335> # Analytic continuation
    a schema:Intangible ;
    schema:name "Analytic continuation"@en ;
    .

<http://id.worldcat.org/fast/808336> # Analytic functions
    a schema:Intangible ;
    schema:name "Analytic functions"@en ;
    .

<http://viaf.org/viaf/108132767> # William Francis Donoghue
    a schema:Person ;
    schema:birthDate "1921" ;
    schema:deathDate "2002" ;
    schema:familyName "Donoghue" ;
    schema:givenName "William Francis" ;
    schema:givenName "William F." ;
    schema:name "William Francis Donoghue" ;
    .

<http://worldcat.org/isbn/9783540065432>
    a schema:ProductModel ;
    schema:isbn "3540065431" ;
    schema:isbn "9783540065432" ;
    .

<http://worldcat.org/isbn/9783642657559>
    a schema:ProductModel ;
    schema:isbn "3642657559" ;
    schema:isbn "9783642657559" ;
    .

<http://www.worldcat.org/oclc/1041036>
    a schema:CreativeWork ;
    rdfs:label "Monotone matrix functions and analytic continuation." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/707452387> ; # Monotone matrix functions and analytic continuation
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.