Linear functional analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
2008
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 324 S. graph. Darst. |
| ISBN: | 9781848000049 9781848000056 |
Internformat
MARC
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|---|---|---|---|
| 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 | ||
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| 035 | |a (DE-599)BVBBV023357017 | ||
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| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
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| 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 | ||
Datensatz im Suchindex
| 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_ | 1806179257842401280 |
| 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 |
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| author | Rynne, Bryan P. 1958- Youngson, Martyn A. 1953- |
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| classification_tum | MAT 460f |
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| 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 |
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| id | DE-604.BV023357017 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:07:38Z |
| indexdate | 2024-08-01T12:06:08Z |
| institution | BVB |
| isbn | 9781848000049 9781848000056 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016540541 |
| oclc_num | 255679030 |
| open_access_boolean | |
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| 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 |
Inhaltsverzeichnis
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 600 R995(2) |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |