Linear functional analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
2008
|
| Edition: | 2. ed. |
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 324 S. graph. Darst. |
| ISBN: | 9781848000049 9781848000056 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV023357017 | ||
| 003 | DE-604 | ||
| 005 | 20090615 | ||
| 007 | t | ||
| 008 | 080623s2008 gw d||| |||| 00||| eng d | ||
| 020 | |a 9781848000049 |9 978-1-84800-004-9 | ||
| 020 | |a 9781848000056 |9 978-1-84800-005-6 | ||
| 035 | |a (OCoLC)255679030 | ||
| 035 | |a (DE-599)BVBBV023357017 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-355 |a DE-824 |a DE-11 |a DE-898 |a DE-862 |a DE-20 |a DE-188 | ||
| 050 | 0 | |a QA320 | |
| 082 | 0 | |a 515.7 | |
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a MAT 460f |2 stub | ||
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Rynne, Bryan P. |d 1958- |e Verfasser |0 (DE-588)121489981 |4 aut | |
| 245 | 1 | 0 | |a Linear functional analysis |c Bryan P. Rynne and Martyn A. Youngson |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London |b Springer |c 2008 | |
| 300 | |a X, 324 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer undergraduate mathematics series | |
| 650 | 4 | |a Functional analysis | |
| 650 | 0 | 7 | |a Lineare Funktionalanalysis |0 (DE-588)4114425-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Funktionalanalysis |0 (DE-588)4114425-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Youngson, Martyn A. |d 1953- |e Verfasser |0 (DE-588)121490009 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016540541&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016540541 | ||
Record in the Search Index
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 600 R995(2) |
| DE-BY-FWS_katkey | 559519 |
| DE-BY-FWS_media_number | 083000514902 |
| _version_ | 1824554421155004417 |
| adam_text | Contents
1.
Preliminaries
............................................... 1
1.1 Linear Algebra........................................... 2
1.2
Metric
Spaces............................................ 11
1.3 Lebesgue Integration...................................... 20
2. Normed Spaces............................................. 31
2.1
Examples of
Normed Spaces............................... 31
2.2
Finite-dimensional
Normed Spaces.......................... 39
2.3 Banach Spaces........................................... 45
3. Inner
Product
Spaces, Hubert Spaces....................... 51
3.1 Inner Products........................................... 51
3.2
Orthogonality
............................................ 60
3.3 Orthogonal
Complements
.................................. 65
3.4
Orthonormal
Bases in Infinite
Dimensions
................... 72
3.5
Fourier Series
............................................ 82
4. Linear Operators........................................... 87
4.1
Continuous
Linear
Transformations.........................
87
4.2
The Norm of a Bounded Linear Operator
.................... 96
4.3
The Space B(X, Y)
.......................................104
4.4
Inverses of Operators
.....................................108
5.
Duality and the
Hahn—
Banach Theorem
....................121
5.1
Dual Spaces
.............................................121
5.2
Sublinear
Funcţionale,
Seminorms and the Hahn-Banach
Theorem
................................................127
χ
Contents
5.3
The Hahn-Banacli Theorem in Normed Spaces
...............132
5.4
The General Hahn-Banach theorem
........................137
5.5
The Second Dual, Reflexive Spaces
and Dual Operators
.......................................144
5.6
Projections and Complementary Subspaces
..................155
5.7
Weak and Weak-* Convergence
............................159
6.
Linear Operators on Hubert Spaces
.........................167
6.1
The Adjoint of an Operator
................................167
6.2
Normal, Self-adjoint and Unitary Operators
..................176
6.3
The Spectrum of an Operator
..............................183
6.4
Positive Operators and Projections
.........................192
7.
Compact Operators
.........................................205
7.1
Compact Operators
.......................................205
7.2
Spectral Theory of Compact Operators
......................216
7.3
Self-adjoint Compact Operators
............................226
8.
Integral and Differential Equations
.........................235
8.1
Fredholm
Integral Equations
...............................235
8.2
Volterra Integral Equations
................................245
8.3
Differential Equations
.....................................247
8.4
Eigenvalue Problems and Green s Functions
..................253
9.
Solutions to Exercises
......................................265
Further Reading
................................................315
References
......................................................317
Notation Index
.................................................319
Index
...................................................... 321
|
| adam_txt |
Contents
1.
Preliminaries
. 1
1.1 Linear Algebra. 2
1.2
Metric
Spaces. 11
1.3 Lebesgue Integration. 20
2. Normed Spaces. 31
2.1
Examples of
Normed Spaces. 31
2.2
Finite-dimensional
Normed Spaces. 39
2.3 Banach Spaces. 45
3. Inner
Product
Spaces, Hubert Spaces. 51
3.1 Inner Products. 51
3.2
Orthogonality
. 60
3.3 Orthogonal
Complements
. 65
3.4
Orthonormal
Bases in Infinite
Dimensions
. 72
3.5
Fourier Series
. 82
4. Linear Operators. 87
4.1
Continuous
Linear
Transformations.
87
4.2
The Norm of a Bounded Linear Operator
. 96
4.3
The Space B(X, Y)
.104
4.4
Inverses of Operators
.108
5.
Duality and the
Hahn—
Banach Theorem
.121
5.1
Dual Spaces
.121
5.2
Sublinear
Funcţionale,
Seminorms and the Hahn-Banach
Theorem
.127
χ
Contents
5.3
The Hahn-Banacli Theorem in Normed Spaces
.132
5.4
The General Hahn-Banach theorem
.137
5.5
The Second Dual, Reflexive Spaces
and Dual Operators
.144
5.6
Projections and Complementary Subspaces
.155
5.7
Weak and Weak-* Convergence
.159
6.
Linear Operators on Hubert Spaces
.167
6.1
The Adjoint of an Operator
.167
6.2
Normal, Self-adjoint and Unitary Operators
.176
6.3
The Spectrum of an Operator
.183
6.4
Positive Operators and Projections
.192
7.
Compact Operators
.205
7.1
Compact Operators
.205
7.2
Spectral Theory of Compact Operators
.216
7.3
Self-adjoint Compact Operators
.226
8.
Integral and Differential Equations
.235
8.1
Fredholm
Integral Equations
.235
8.2
Volterra Integral Equations
.245
8.3
Differential Equations
.247
8.4
Eigenvalue Problems and Green's Functions
.253
9.
Solutions to Exercises
.265
Further Reading
.315
References
.317
Notation Index
.319
Index
. 321 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Rynne, Bryan P. 1958- Youngson, Martyn A. 1953- |
| author_GND | (DE-588)121489981 (DE-588)121490009 |
| author_facet | Rynne, Bryan P. 1958- Youngson, Martyn A. 1953- |
| author_role | aut aut |
| author_sort | Rynne, Bryan P. 1958- |
| author_variant | b p r bp bpr m a y ma may |
| building | Verbundindex |
| bvnumber | BV023357017 |
| callnumber-first | Q - Science |
| callnumber-label | QA320 |
| callnumber-raw | QA320 |
| callnumber-search | QA320 |
| callnumber-sort | QA 3320 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)255679030 (DE-599)BVBBV023357017 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01626nam a2200433 c 4500</leader><controlfield tag="001">BV023357017</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090615 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080623s2008 gw d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781848000049</subfield><subfield code="9">978-1-84800-004-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781848000056</subfield><subfield code="9">978-1-84800-005-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)255679030</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023357017</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</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="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-862</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA320</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.7</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 460f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rynne, Bryan P.</subfield><subfield code="d">1958-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)121489981</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Linear functional analysis</subfield><subfield code="c">Bryan P. Rynne and Martyn A. Youngson</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">Springer</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 324 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Springer undergraduate mathematics series</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare Funktionalanalysis</subfield><subfield code="0">(DE-588)4114425-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineare Funktionalanalysis</subfield><subfield code="0">(DE-588)4114425-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Youngson, Martyn A.</subfield><subfield code="d">1953-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)121490009</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016540541&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016540541</subfield></datafield></record></collection> |
| id | DE-604.BV023357017 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:07:38Z |
| indexdate | 2025-02-20T06:51:30Z |
| institution | BVB |
| isbn | 9781848000049 9781848000056 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016540541 |
| oclc_num | 255679030 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-11 DE-898 DE-BY-UBR DE-862 DE-BY-FWS DE-20 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-11 DE-898 DE-BY-UBR DE-862 DE-BY-FWS DE-20 DE-188 |
| physical | X, 324 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spellingShingle | Rynne, Bryan P. 1958- Youngson, Martyn A. 1953- Linear functional analysis Functional analysis Lineare Funktionalanalysis (DE-588)4114425-9 gnd |
| subject_GND | (DE-588)4114425-9 |
| title | Linear functional analysis |
| title_auth | Linear functional analysis |
| title_exact_search | Linear functional analysis |
| title_exact_search_txtP | Linear functional analysis |
| title_full | Linear functional analysis Bryan P. Rynne and Martyn A. Youngson |
| title_fullStr | Linear functional analysis Bryan P. Rynne and Martyn A. Youngson |
| title_full_unstemmed | Linear functional analysis Bryan P. Rynne and Martyn A. Youngson |
| title_short | Linear functional analysis |
| title_sort | linear functional analysis |
| topic | Functional analysis Lineare Funktionalanalysis (DE-588)4114425-9 gnd |
| topic_facet | Functional analysis Lineare Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016540541&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rynnebryanp linearfunctionalanalysis AT youngsonmartyna linearfunctionalanalysis |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 600 R995(2) |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |