Elementary Functional Analysis / / Marat V. Markin.
While there is a plethora of excellent, but mostly "tell-it-all'' books on the subject, this one is intended to take a unique place in what today seems to be a still wide open niche for an introductory text on the basics of functional analysis to be taught within the existing constrai...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 |
---|---|
VerfasserIn: | |
MitwirkendeR: | |
Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2018] ©2018 |
Year of Publication: | 2018 |
Language: | English |
Series: | De Gruyter Textbook
|
Online Access: | |
Physical Description: | 1 online resource (XVI, 314 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9783110614039 |
---|---|
lccn |
2018950580 |
ctrlnum |
(DE-B1597)498784 (OCoLC)1059274371 |
collection |
bib_alma |
record_format |
marc |
spelling |
Markin, Marat V., author. aut http://id.loc.gov/vocabulary/relators/aut Elementary Functional Analysis / Marat V. Markin. Berlin ; Boston : De Gruyter, [2018] ©2018 1 online resource (XVI, 314 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Metric Spaces -- 3. Normed Vector and Banach Spaces -- 4. Inner Product and Hilbert Spaces -- 5. Linear Operators and Functionals -- 6. Three Fundamental Principles of Linear Functional Analysis -- 7. Duality and Reflexivity -- A The Axiom of Choice and Equivalents -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star While there is a plethora of excellent, but mostly "tell-it-all'' books on the subject, this one is intended to take a unique place in what today seems to be a still wide open niche for an introductory text on the basics of functional analysis to be taught within the existing constraints of the standard, for the United States, one-semester graduate curriculum (fifteen weeks with two seventy-five-minute lectures per week). The book consists of seven chapters and an appendix taking the reader from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), through the basics of linear operators and functionals, the three fundamental principles (the Hahn-Banach Theorem, the Uniform Boundedness Principle, the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems) with their numerous profound implications and certain interesting applications, to the elements of the duality and reflexivity theory. Chapter 1 outlines some necessary preliminaries, while the Appendix gives a concise discourse on the celebrated Axiom of Choice, its equivalents (the Hausdorff Maximal Principle, Zorn's Lemma, and Zermello's Well-Ordering Principle), and ordered sets. Being designed as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. It contains 112 Problems, which are indispensable for understanding and moving forward. Many important statements are given as problems, a lot of these are frequently referred to and used in the main body. There are also 376 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in necessary details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problem and exercises being supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying every definition and virtually each statement to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. The prerequisites are set intentionally quite low, the students not being assumed to have taken graduate courses in real or complex analysis and general topology, to make the course accessible and attractive to a wider audience of STEM (science, technology, engineering, and mathematics) graduate students or advanced undergraduates with a solid background in calculus and linear algebra. With proper attention given to applications, plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester graduate course on the fundamentals of functional analysis for students in mathematics, physics, computer science, and engineering. ContentsPreliminariesMetric SpacesNormed Vector and Banach SpacesInner Product and Hilbert SpacesLinear Operators and FunctionalsThree Fundamental Principles of Linear Functional AnalysisDuality and ReflexivityThe Axiom of Choice and Equivalents Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Functional analysis. Banach-Raum. Funktionalanalysis. Hahn-Banach-Fortsetzungssatz. Hilbert-Raum. Metrischer Raum. MATHEMATICS / Functional Analysis. bisacsh Markin, Marat V., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 9783110719550 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English 9783110604252 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 9783110603255 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English 9783110604191 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 9783110603194 ZDB-23-DMA EPUB 9783110614091 print 9783110613919 https://doi.org/10.1515/9783110614039 https://www.degruyter.com/isbn/9783110614039 Cover https://www.degruyter.com/cover/covers/9783110614039.jpg |
language |
English |
format |
eBook |
author |
Markin, Marat V., Markin, Marat V., |
spellingShingle |
Markin, Marat V., Markin, Marat V., Elementary Functional Analysis / De Gruyter Textbook Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Metric Spaces -- 3. Normed Vector and Banach Spaces -- 4. Inner Product and Hilbert Spaces -- 5. Linear Operators and Functionals -- 6. Three Fundamental Principles of Linear Functional Analysis -- 7. Duality and Reflexivity -- A The Axiom of Choice and Equivalents -- Bibliography -- Index |
author_facet |
Markin, Marat V., Markin, Marat V., Markin, Marat V., Markin, Marat V., |
author_variant |
m v m mv mvm m v m mv mvm |
author_role |
VerfasserIn VerfasserIn |
author2 |
Markin, Marat V., Markin, Marat V., |
author2_variant |
m v m mv mvm m v m mv mvm |
author2_role |
MitwirkendeR MitwirkendeR |
author_sort |
Markin, Marat V., |
title |
Elementary Functional Analysis / |
title_full |
Elementary Functional Analysis / Marat V. Markin. |
title_fullStr |
Elementary Functional Analysis / Marat V. Markin. |
title_full_unstemmed |
Elementary Functional Analysis / Marat V. Markin. |
title_auth |
Elementary Functional Analysis / |
title_alt |
Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Metric Spaces -- 3. Normed Vector and Banach Spaces -- 4. Inner Product and Hilbert Spaces -- 5. Linear Operators and Functionals -- 6. Three Fundamental Principles of Linear Functional Analysis -- 7. Duality and Reflexivity -- A The Axiom of Choice and Equivalents -- Bibliography -- Index |
title_new |
Elementary Functional Analysis / |
title_sort |
elementary functional analysis / |
series |
De Gruyter Textbook |
series2 |
De Gruyter Textbook |
publisher |
De Gruyter, |
publishDate |
2018 |
physical |
1 online resource (XVI, 314 p.) |
contents |
Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Metric Spaces -- 3. Normed Vector and Banach Spaces -- 4. Inner Product and Hilbert Spaces -- 5. Linear Operators and Functionals -- 6. Three Fundamental Principles of Linear Functional Analysis -- 7. Duality and Reflexivity -- A The Axiom of Choice and Equivalents -- Bibliography -- Index |
isbn |
9783110614039 9783110719550 9783110604252 9783110603255 9783110604191 9783110603194 9783110614091 9783110613919 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA320 |
callnumber-sort |
QA 3320 M324 42018 |
url |
https://doi.org/10.1515/9783110614039 https://www.degruyter.com/isbn/9783110614039 https://www.degruyter.com/cover/covers/9783110614039.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.7 |
dewey-sort |
3515.7 |
dewey-raw |
515.7 |
dewey-search |
515.7 |
doi_str_mv |
10.1515/9783110614039 |
oclc_num |
1059274371 |
work_keys_str_mv |
AT markinmaratv elementaryfunctionalanalysis |
status_str |
n |
ids_txt_mv |
(DE-B1597)498784 (OCoLC)1059274371 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 |
is_hierarchy_title |
Elementary Functional Analysis / |
container_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 |
author2_original_writing_str_mv |
noLinkedField noLinkedField |
_version_ |
1806144478405197824 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06886nam a22008775i 4500</leader><controlfield tag="001">9783110614039</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20210830012106.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">210830t20182018gw fo d z eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2018950580</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110614039</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783110614039</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)498784</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1059274371</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="050" ind1="0" ind2="0"><subfield code="a">QA320</subfield><subfield code="b">.M324 2018</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">Internet Access</subfield><subfield code="b">AEU</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT037000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">515.7</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Markin, Marat V., </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elementary Functional Analysis /</subfield><subfield code="c">Marat V. Markin.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ;</subfield><subfield code="a">Boston : </subfield><subfield code="b">De Gruyter, </subfield><subfield code="c">[2018]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2018</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (XVI, 314 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">De Gruyter Textbook</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">1. Preliminaries -- </subfield><subfield code="t">2. Metric Spaces -- </subfield><subfield code="t">3. Normed Vector and Banach Spaces -- </subfield><subfield code="t">4. Inner Product and Hilbert Spaces -- </subfield><subfield code="t">5. Linear Operators and Functionals -- </subfield><subfield code="t">6. Three Fundamental Principles of Linear Functional Analysis -- </subfield><subfield code="t">7. Duality and Reflexivity -- </subfield><subfield code="t">A The Axiom of Choice and Equivalents -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">While there is a plethora of excellent, but mostly "tell-it-all'' books on the subject, this one is intended to take a unique place in what today seems to be a still wide open niche for an introductory text on the basics of functional analysis to be taught within the existing constraints of the standard, for the United States, one-semester graduate curriculum (fifteen weeks with two seventy-five-minute lectures per week). The book consists of seven chapters and an appendix taking the reader from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), through the basics of linear operators and functionals, the three fundamental principles (the Hahn-Banach Theorem, the Uniform Boundedness Principle, the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems) with their numerous profound implications and certain interesting applications, to the elements of the duality and reflexivity theory. Chapter 1 outlines some necessary preliminaries, while the Appendix gives a concise discourse on the celebrated Axiom of Choice, its equivalents (the Hausdorff Maximal Principle, Zorn's Lemma, and Zermello's Well-Ordering Principle), and ordered sets. Being designed as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. It contains 112 Problems, which are indispensable for understanding and moving forward. Many important statements are given as problems, a lot of these are frequently referred to and used in the main body. There are also 376 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in necessary details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problem and exercises being supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying every definition and virtually each statement to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. The prerequisites are set intentionally quite low, the students not being assumed to have taken graduate courses in real or complex analysis and general topology, to make the course accessible and attractive to a wider audience of STEM (science, technology, engineering, and mathematics) graduate students or advanced undergraduates with a solid background in calculus and linear algebra. With proper attention given to applications, plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester graduate course on the fundamentals of functional analysis for students in mathematics, physics, computer science, and engineering. ContentsPreliminariesMetric SpacesNormed Vector and Banach SpacesInner Product and Hilbert SpacesLinear Operators and FunctionalsThree Fundamental Principles of Linear Functional AnalysisDuality and ReflexivityThe Axiom of Choice and Equivalents</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Functional analysis.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Banach-Raum.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Funktionalanalysis.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hahn-Banach-Fortsetzungssatz.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hilbert-Raum.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Metrischer Raum.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Functional Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Markin, Marat V., </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">DG Plus eBook-Package 2018</subfield><subfield code="z">9783110719550</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2018 English</subfield><subfield code="z">9783110604252</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2018</subfield><subfield code="z">9783110603255</subfield><subfield code="o">ZDB-23-DGG</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE Mathematics 2018 English</subfield><subfield code="z">9783110604191</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE Mathematics 2018</subfield><subfield code="z">9783110603194</subfield><subfield code="o">ZDB-23-DMA</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">EPUB</subfield><subfield code="z">9783110614091</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9783110613919</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9783110614039</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9783110614039</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/cover/covers/9783110614039.jpg</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-060419-1 EBOOK PACKAGE Mathematics 2018 English</subfield><subfield code="b">2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-060425-2 EBOOK PACKAGE COMPLETE 2018 English</subfield><subfield code="b">2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-071955-0 DG Plus eBook-Package 2018</subfield><subfield code="b">2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_DGALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="b">2017</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DMA</subfield><subfield code="b">2018</subfield></datafield></record></collection> |