skip to content
Topological vector spaces and their applications Preview this item
ClosePreview this item
Checking...

Topological vector spaces and their applications

Author: V I Bogachev; O G Smolyanov
Publisher: Cham, Switzerland : Springer, 2017.
Series: Springer monographs in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in  Read more...
Rating:

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

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

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

Details

Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V I Bogachev; O G Smolyanov
ISBN: 9783319571171 3319571176 3319571168 9783319571164
OCLC Number: 987790956
Description: 1 online resource.
Contents: Preface; 1 Introduction to the theory of topological vector spaces; 1.1. Linear spaces and topology; 1.2. Basic definitions; 1.3. Examples; 1.4. Convex sets; 1.5. Finite-dimensional and normable spaces; 1.6. Metrizability; 1.7. Completeness and completions; 1.8. Compact and precompact sets; 1.9. Linear operators; 1.10. The Hahn-Banach theorem: geometric form; 1.11. The Hahn-Banach theorem: the analytic form; 1.12. Complements and exercises; 1.12(i). Uniform spaces; 1.12(ii). Convex compact sets; 1.12(iii). Fixed point theorems; 1.12(iv). Sequence spaces 1.12(v). Duals to Banach spaces1.12(vi). Separability properties; 1.12(vii). Continuous selections and extensions; Exercises; 2 Methods of constructing topological vector spaces; 2.1. Projective topologies; 2.2. Examples of projective limits; 2.3. Inductive topologies; 2.4. Examples of inductive limits; 2.5. Grothendieck's construction; 2.6. Strict inductive limits; 2.7. Inductive limits with compact embeddings; 2.8. Tensor products; 2.9. Nuclear spaces; 2.10. Complements and exercises; 2.10(i). Properties of the spaces D and D ; 2.10(ii). Absolutely summing operators 2.10(iii). Local completenessExercises; 3 Duality; 3.1. Polars; 3.2. Topologies compatible with duality; 3.3. Adjoint operators; 3.4. Weak compactness; 3.5. Barrelled spaces; 3.6. Bornological spaces; 3.7. The strong topology and reflexivity; 3.8. Criteria for completeness; 3.9. The closed graph theorem; 3.10. Compact operators; 3.11. The Fredholm alternative; 3.12. Complements and exercises; 3.12(i). Baire spaces; 3.12(ii). The Borel graph theorem; 3.12(iii). Bounding sets; 3.12(iv). The James theorem; 3.12(v). Topological properties of locally convex spaces 3.12(vi). The Eberlein-Šmulian properties3.12(vii). Schauder bases; 3.12(viii). Minimal spaces and powers of the real line; Exercises; 4 Differential calculus; 4.1. Differentiability with respect to systems of sets; 4.2. Examples; 4.3. Differentiability and continuity; 4.4. Differentiability and continuity along a subspace; 4.5. The derivative of a composition; 4.6. The mean value theorem; 4.7. Taylor's formula; 4.8. Partial derivatives; 4.9. Inversion of Taylor's formula and the chain rule; 4.10. Complements and exercises; 4.10(i). The inverse function theorem; 4.10(ii). Polynomials 4.10(iii). Ordinary differential equations in locally convex spaces4.10(iv). Passage to the limit in derivatives; 4.10(v). Completeness of spaces of smooth mappings; 4.10(vi). Differentiability via pseudotopologies; 4.10(vii). Smooth functions on Banach spaces; Exercises; 5 Measures on linear spaces; 5.1. Cylindrical sets; 5.2. Measures on topological spaces; 5.3. Transformations and convergence of measures; 5.4. Cylindrical measures; 5.5. The Fourier transform; 5.6. Covariance operators and means of measures; 5.7. Gaussian measures; 5.8. Quasi-measures; 5.9. Sufficient topologies
Series Title: Springer monographs in mathematics.
Responsibility: V.I. Bogachev, O.G. Smolyanov.

Abstract:

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Reviews

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

Tags

Be the first.

Similar Items

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/987790956> # Topological vector spaces and their applications
    a schema:Book, schema:CreativeWork, schema:MediaObject ;
    library:oclcnum "987790956" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/sz> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/4152464319#Topic/vector_spaces> ; # Vector spaces
    schema:about <http://dewey.info/class/512.52/e23/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/4152464319#Topic/mathematics_algebra_intermediate> ; # MATHEMATICS / Algebra / Intermediate
    schema:author <http://experiment.worldcat.org/entity/work/data/4152464319#Person/bogachev_v_i_vladimir_igorevich_1961> ; # Vladimir Igorevich Bogachev
    schema:author <http://experiment.worldcat.org/entity/work/data/4152464319#Person/smolyanov_o_g> ; # O. G. Smolyanov
    schema:bookFormat schema:EBook ;
    schema:datePublished "2017" ;
    schema:description "Preface; 1 Introduction to the theory of topological vector spaces; 1.1. Linear spaces and topology; 1.2. Basic definitions; 1.3. Examples; 1.4. Convex sets; 1.5. Finite-dimensional and normable spaces; 1.6. Metrizability; 1.7. Completeness and completions; 1.8. Compact and precompact sets; 1.9. Linear operators; 1.10. The Hahn-Banach theorem: geometric form; 1.11. The Hahn-Banach theorem: the analytic form; 1.12. Complements and exercises; 1.12(i). Uniform spaces; 1.12(ii). Convex compact sets; 1.12(iii). Fixed point theorems; 1.12(iv). Sequence spaces"@en ;
    schema:description "This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/4152464319> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://worldcat.org/issn/1439-7382> ; # Springer monographs in mathematics,
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/4152464319#Series/springer_monographs_in_mathematics> ; # Springer monographs in mathematics.
    schema:isSimilarTo <http://worldcat.org/entity/work/data/4152464319#CreativeWork/> ;
    schema:name "Topological vector spaces and their applications"@en ;
    schema:productID "987790956" ;
    schema:url <http://link.springer.com/10.1007/978-3-319-57117-1> ;
    schema:url <http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-57117-1> ;
    schema:url <https://login.proxy.lib.strath.ac.uk/login?url=http://link.springer.com/10.1007/978-3-319-57117-1> ;
    schema:url <http://public.eblib.com/choice/PublicFullRecord.aspx?p=4862526> ;
    schema:url <https://link.springer.com/openurl?genre=book&isbn=978-3-319-57116-4> ;
    schema:url <https://grinnell.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-57117-1> ;
    schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1520792> ;
    schema:url <http://dx.doi.org/10.1007/978-3-319-57117-1> ;
    schema:workExample <http://worldcat.org/isbn/9783319571171> ;
    schema:workExample <http://worldcat.org/isbn/9783319571164> ;
    schema:workExample <http://dx.doi.org/10.1007/978-3-319-57117-1> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/987790956> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/4152464319#Person/bogachev_v_i_vladimir_igorevich_1961> # Vladimir Igorevich Bogachev
    a schema:Person ;
    schema:birthDate "1961" ;
    schema:familyName "Bogachev" ;
    schema:givenName "Vladimir Igorevich" ;
    schema:givenName "V. I." ;
    schema:name "Vladimir Igorevich Bogachev" ;
    .

<http://experiment.worldcat.org/entity/work/data/4152464319#Person/smolyanov_o_g> # O. G. Smolyanov
    a schema:Person ;
    schema:familyName "Smolyanov" ;
    schema:givenName "O. G." ;
    schema:name "O. G. Smolyanov" ;
    .

<http://experiment.worldcat.org/entity/work/data/4152464319#Series/springer_monographs_in_mathematics> # Springer monographs in mathematics.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/987790956> ; # Topological vector spaces and their applications
    schema:name "Springer monographs in mathematics." ;
    .

<http://experiment.worldcat.org/entity/work/data/4152464319#Topic/mathematics_algebra_intermediate> # MATHEMATICS / Algebra / Intermediate
    a schema:Intangible ;
    schema:name "MATHEMATICS / Algebra / Intermediate"@en ;
    .

<http://link.springer.com/10.1007/978-3-319-57117-1>
    rdfs:comment "from Springer" ;
    rdfs:comment "(Unlimited Concurrent Users)" ;
    .

<http://worldcat.org/entity/work/data/4152464319#CreativeWork/>
    a schema:CreativeWork ;
    schema:description "Printed edition:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/987790956> ; # Topological vector spaces and their applications
    .

<http://worldcat.org/isbn/9783319571164>
    a schema:ProductModel ;
    schema:isbn "3319571168" ;
    schema:isbn "9783319571164" ;
    .

<http://worldcat.org/isbn/9783319571171>
    a schema:ProductModel ;
    schema:isbn "3319571176" ;
    schema:isbn "9783319571171" ;
    .

<http://worldcat.org/issn/1439-7382> # Springer monographs in mathematics,
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/987790956> ; # Topological vector spaces and their applications
    schema:issn "1439-7382" ;
    schema:name "Springer monographs in mathematics," ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

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