Theorems and problems in functional analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
New York [u.a.]
Springer
1982
|
| Series: | Problem books in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | IX, 347 S. |
| ISBN: | 038790638X 354090638X |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002269936 | ||
| 003 | DE-604 | ||
| 005 | 20220722 | ||
| 007 | t | ||
| 008 | 890928s1982 |||| 00||| eng d | ||
| 020 | |a 038790638X |9 0-387-90638-X | ||
| 020 | |a 354090638X |9 3-540-90638-X | ||
| 035 | |a (OCoLC)8114713 | ||
| 035 | |a (DE-599)BVBBV002269936 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h rus | |
| 049 | |a DE-91 |a DE-384 |a DE-703 |a DE-739 |a DE-355 |a DE-824 |a DE-29T |a DE-20 |a DE-19 |a DE-706 |a DE-634 |a DE-11 |a DE-188 |a DE-83 | ||
| 050 | 0 | |a QA320 | |
| 082 | 0 | |a 515.7 |2 19 | |
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a 46-01 |2 msc | ||
| 084 | |a 43-01 |2 msc | ||
| 084 | |a 28-01 |2 msc | ||
| 084 | |a 00A07 |2 msc | ||
| 084 | |a 42-01 |2 msc | ||
| 084 | |a 47-01 |2 msc | ||
| 084 | |a MAT 460f |2 stub | ||
| 100 | 1 | |a Kirillov, Aleksandr A. |d 1936- |e Verfasser |0 (DE-588)124974953 |4 aut | |
| 240 | 1 | 0 | |a Teoremy i zadači funkcional'nogo analiza |
| 245 | 1 | 0 | |a Theorems and problems in functional analysis |c A. A. Kirillov ; A. D. Gvishiani |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1982 | |
| 300 | |a IX, 347 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Problem books in mathematics | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 7 | |a Functionaalanalyse |2 gtt | |
| 650 | 4 | |a Functional analysis | |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143389-0 |a Aufgabensammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gvišiani, Aleksej D. |d 1948- |e Verfasser |0 (DE-588)118197169 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001491467&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001491467 | ||
Record in the Search Index
| _version_ | 1804116727656611840 |
|---|---|
| adam_text | Contents
Chapter I
Concepts from Set Theory and Topology
§1. Relations. The Axiom of Choice and Zorn s Lemma
Theory (3). Problems (139). Hints (233).
§2. Completions
Theory (6). Problems (142). Hints (237).
§3. Categories and Functors
Theory (8). Problems (145). Hints (240).
Chapter II
Theory of Measures and Integrals
§1. Measure Theory
1. Algebras of Sets
Theory (12). Problems (150). Hints (244).
2. Extension of a Measure
Theory (13). Problems (152). Hints (246).
3. Constructions of Measures
Theory (18). Problems (154). Hints (250).
§2. Measurable Functions
1. Properties of Measurable Functions
Theory (22). Problems (156). Hints (253).
2. Convergence of Measurable Functions
Theory (23). Problems (158). Hints (255).
vii
viii Contents
§3. Integrals
1. The Lebesgue Integral
Theory (24). Problems (160). Hints (257).
2. Functions of Bounded Variation and the Lebesque Stieltjes
Integral
Theory (28). Problems (163). Hints (263).
3. Properties of the Lebesgue Integral
Theory (31). Problems (166). Hints (266).
Chapter III
Linear Topological Spaces and Linear Operators
§1. General Theory
1. Topology, Convexity, and Seminorms
Theory (38). Problems (170). Hints (271).
2. Dual Spaces
Theory (42). Problems (172). Hints (274).
3. The Hahn Banach Theorem
Theory (43). Problems (174). Hints (276).
4. Banach Spaces
Theory (46). Problems (176). Hints (279).
§2. Linear Operators
1. The Space of Linear Operators
Theory (50). Problems (178). Hints (282).
2. Compact Sets and Compact Operators
Theory (54). Problems (180). Hints (284).
3. The Theory of Fredholm Operators
Theory (59). Problems (181). Hints (286).
§3. Function Spaces and Generalized Functions
1. Spaces of Integrable Functions
Theory (66). Problems (185). Hints (288).
2. Spaces of Continuous Functions
Theory (68). Problems (187). Hints (291).
3. Spaces of Smooth Functions
Theory (69). Problems (189). Hints (296).
4. Generalized Functions
Theory (78). Problems (192). Hints (298).
5. Operations on Generalized Functions
Theory (81). Problems (195). Hints (300).
§4. Hilbert Spaces
1. The Geometry of Hilbert Spaces
Theory (84). Problems (197). Hints (303).
2. Operators on a Hilbert Space
Theory (90). Problems (200). Hints (305).
Contents ix
Chapter IV
The Fourier Transformation and
Elements of Harmonic Analysis
§1. Convolutions on an Abelian Group
1. Convolutions of Test Functions
Theory (95). Problems (204). Hints (309).
2. Convolutions of Generalized Functions
Theory (99). Problems (206). Hints (311).
§2. The Fourier Transformation
1. Characters on an Abelian Group
Theory (104). Problems (209). Hints (313).
2. Fourier Series
Theory (108). Problems (211). Hints (315).
3. The Fourier Integral
Theory (110). Problems (213). Hints (318).
4. Fourier Transformation of Generalized Functions
Theory (114). Problems (216). Hints (322).
Chapter V
The Spectral Theory of Operators
§1. The Functional Calculus
1. Functions of Operators in a Finite Dimensional Space
Theory (116). Problems (219). Hints (325).
2. Functions of Bounded Selfadjoint Operators
Theory (118). Problems (222). Hints (327).
3. Unbounded Selfadjoint Operators
Theory (124). Problems (223). Hints (328).
§2. Spectral Decomposition of Operators
1. Reduction of an Operator to the Form of Multiplication
by a Function
Theory (127). Problems (225). Hints (330).
2. The Spectral Theorem
Theory (131). Problems (227). Hints (332).
List of Notation 335
Bibliography 339
Subject Index 343
|
| any_adam_object | 1 |
| author | Kirillov, Aleksandr A. 1936- Gvišiani, Aleksej D. 1948- |
| author_GND | (DE-588)124974953 (DE-588)118197169 |
| author_facet | Kirillov, Aleksandr A. 1936- Gvišiani, Aleksej D. 1948- |
| author_role | aut aut |
| author_sort | Kirillov, Aleksandr A. 1936- |
| author_variant | a a k aa aak a d g ad adg |
| building | Verbundindex |
| bvnumber | BV002269936 |
| 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)8114713 (DE-599)BVBBV002269936 |
| 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 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02020nam a2200541 c 4500</leader><controlfield tag="001">BV002269936</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220722 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1982 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">038790638X</subfield><subfield code="9">0-387-90638-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">354090638X</subfield><subfield code="9">3-540-90638-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)8114713</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002269936</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="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</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><subfield code="2">19</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">46-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">43-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">28-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">00A07</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">42-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 460f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kirillov, Aleksandr A.</subfield><subfield code="d">1936-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)124974953</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Teoremy i zadači funkcional'nogo analiza</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Theorems and problems in functional analysis</subfield><subfield code="c">A. A. Kirillov ; A. D. Gvishiani</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1982</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 347 S.</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">Problem books in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus dem Russ. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse fonctionnelle</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse fonctionnelle</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Functionaalanalyse</subfield><subfield code="2">gtt</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">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4143389-0</subfield><subfield code="a">Aufgabensammlung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</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">Gvišiani, Aleksej D.</subfield><subfield code="d">1948-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)118197169</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=001491467&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:BVB01-001491467</subfield></datafield></record></collection> |
| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV002269936 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:06Z |
| institution | BVB |
| isbn | 038790638X 354090638X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001491467 |
| oclc_num | 8114713 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-83 |
| owner_facet | DE-91 DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-83 |
| physical | IX, 347 S. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer |
| record_format | marc |
| series2 | Problem books in mathematics |
| spelling | Kirillov, Aleksandr A. 1936- Verfasser (DE-588)124974953 aut Teoremy i zadači funkcional'nogo analiza Theorems and problems in functional analysis A. A. Kirillov ; A. D. Gvishiani New York [u.a.] Springer 1982 IX, 347 S. txt rdacontent n rdamedia nc rdacarrier Problem books in mathematics Aus dem Russ. übers. Analyse fonctionnelle Analyse fonctionnelle ram Functionaalanalyse gtt Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Gvišiani, Aleksej D. 1948- Verfasser (DE-588)118197169 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001491467&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kirillov, Aleksandr A. 1936- Gvišiani, Aleksej D. 1948- Theorems and problems in functional analysis Analyse fonctionnelle Analyse fonctionnelle ram Functionaalanalyse gtt Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4143389-0 |
| title | Theorems and problems in functional analysis |
| title_alt | Teoremy i zadači funkcional'nogo analiza |
| title_auth | Theorems and problems in functional analysis |
| title_exact_search | Theorems and problems in functional analysis |
| title_full | Theorems and problems in functional analysis A. A. Kirillov ; A. D. Gvishiani |
| title_fullStr | Theorems and problems in functional analysis A. A. Kirillov ; A. D. Gvishiani |
| title_full_unstemmed | Theorems and problems in functional analysis A. A. Kirillov ; A. D. Gvishiani |
| title_short | Theorems and problems in functional analysis |
| title_sort | theorems and problems in functional analysis |
| topic | Analyse fonctionnelle Analyse fonctionnelle ram Functionaalanalyse gtt Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analyse fonctionnelle Functionaalanalyse Functional analysis Funktionalanalysis Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001491467&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kirillovaleksandra teoremyizadacifunkcionalnogoanaliza AT gvisianialeksejd teoremyizadacifunkcionalnogoanaliza AT kirillovaleksandra theoremsandproblemsinfunctionalanalysis AT gvisianialeksejd theoremsandproblemsinfunctionalanalysis |