Distributions and operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Series: | Graduate texts in mathematics
252 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 461 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387848945 |
Staff View
MARC
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| 245 | 1 | 0 | |a Distributions and operators |c Gerd Grubb |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XII, 461 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 252 | |
| 650 | 4 | |a Hilbert, Espace de | |
| 650 | 4 | |a Théorie des distributions (Analyse fonctionnelle) | |
| 650 | 4 | |a Théorie des opérateurs | |
| 650 | 4 | |a Hilbert space | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Theory of distributions (Functional analysis) | |
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| 830 | 0 | |a Graduate texts in mathematics |v 252 |w (DE-604)BV000000067 |9 252 | |
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Record in the Search Index
| _version_ | 1811034388881735680 |
|---|---|
| adam_text |
Contents
Preface
.
v
Part I Distributions and derivatives
1
Motivation and overview
. 3
1.1
Introduction
. 3
1.2
On the definition of distributions
. 6
2
Function spaces and approximation
. 9
2.1
The space of test functions
. 9
2.2
Some other function spaces
. 16
2.3
Approximation theorems
. 17
2.4
Partitions of unity
. 23
Exercises for Chapter
2. 24
3
Distributions. Examples and rules of calculus
. 27
3.1
Distributions
. 27
3.2
Rules of calculus for distributions
. 31
3.3
Distributions with compact support
. 36
3.4
Convolutions and coordinate changes
. 40
3.5
The calculation rules and the weak* topology on
3'. 46
Exercises for Chapter
3. 50
Part II Extensions and applications
4
Realizations and Sobolev spaces
.,. 57
4.1
Realizations of differential operators
. 57
4.2
Sobolev spaces
. 61
4.3
The one-dimensional case
. 68
4.4
Boundary value problems in higher dimensions
. 77
Exercises for Chapter
4. 86
x
Contents
5
Fourier transformation of distributions
. 05
5.1
Rapidly decreasing functions
. 95
5.2
Temperate distributions
.103
5.3
The Fourier transform on
З"
.105
5.4
Homogeneity
.110
5.5
Application to the Laplace operator
.114
5.6
Distributions associated with nonintegrable functions
.116
Exercises for Chapter
5.120
6
Applications to differential operators. The Sobolev theorem
123
6.1
Differential and pseudodifferential operators on R™
.123
6.2
Sobolev spaces of arbitrary real order. The Sobolev theorem
. 127
6.3
Dualities between Sobolev spaces. The Structure theorem
. 132
6.4
Regularity theory for elliptic differential equations
.138
Exercises for Chapter
6.144
Miscellaneous exercises (exam problems)
.147
Part III Pseudodifferential operators
7
Pseudodifferential operators on open sets
.163
7.1
Symbols and operators, mapping properties
. 163
7.2
Negligible operators
. 172
7.3
Composition rules
. 178
7.4
Elliptic pseudodifferential operators
. 183
7.5
Strongly elliptic operators, the
Gårding
inequality
. 189
Exercises for Chapter
7. 193
8
Pseudodifferential operators on manifolds, index of
elliptic operators
.195
8.1
Coordinate changes
.195
8.2
Operators on manifolds
.197
8.3
Fredholm
theory, the index
.208
Exercises for Chapter
8.215
Part IV Boundary value problems
9
Boundary value problems in a constant-coefficient case
. 219
9.1
Boundary maps for the half-space
.219
9.2
The Dirichlet problem for I
-
Δ
on the half-space
.228
9.3
The Neumann problem for I
—
Δ
on the half-space
.234
9.4
Other realizations of I
-
A
.236
9.5
Variable-coefficient cases, higher orders, systems
.
24(i
Exercises for Chapter
9.248
Contents
xi
10 Pseudodifferential
boundary operators
.251
10.1
The real formulation
.251
10.2
Fourier transform and Laguerre expansion of
<5^+
.266
10.3
The complex formulation
.275
10.4
Composition rules
.281
10.5
Continuity
.289
10.6
Elliptic ^dbo's
.296
Exercises for Chapter
10.300
11
Pseudodifferential methods for boundary value problems
. 305
11.1
The
Calderón
projector
.305
11.2
Application to boundary value problems
.317
11.3
The solution operator for the Dirichlet problem
.320
Exercises for Chapter
11.326
Part V Topics on Hubert space operators
12
Unbounded linear operators
.337
12.1
Unbounded operators in Banach spaces
.337
12.2
Unbounded operators in Hubert spaces
.340
12.3
Symmetric, selfadjoint and semibounded operators
.343
12.4
Operators associated with sesquilinear forms
.350
12.5
The
Friedrichs
extension
.359
12.6
More on variational operators
.361
Exercises for Chapter
12.364
13
Families of extensions
.373
13.1
A universal parametrization of extensions
.373
13.2
The symmetric case
.383
13.3
Consequences for resolvents
.393
13.4
Boundary triplets and M-functions
.397
Exercises for Chapter
13.402
14
Semigroups of operators
.405
14.1
Evolution equations
.405
14.2
Contraction semigroups in Banach spaces
.409
14.3
Contraction semigroups in Hubert spaces
.416
14.4
Applications
.419
Exercises for Chapter
14.421
A Some notation and prerequisites
.423
Exercises for Appendix A
.429
xii Contents
В
Topological
vector
spaces
. 431
B.I
Fréchet
spaces
. 431
В.
2
Inductive limits of
Fréchet
spaces
. 441
Exercises for Appendix
В
. 443
С
Function spaces on sets with smooth boundary
.447
Exercises for Appendix
G
.450
Bibliography
.451
Index
.457 |
| adam_txt |
Contents
Preface
.
v
Part I Distributions and derivatives
1
Motivation and overview
. 3
1.1
Introduction
. 3
1.2
On the definition of distributions
. 6
2
Function spaces and approximation
. 9
2.1
The space of test functions
. 9
2.2
Some other function spaces
. 16
2.3
Approximation theorems
. 17
2.4
Partitions of unity
. 23
Exercises for Chapter
2. 24
3
Distributions. Examples and rules of calculus
. 27
3.1
Distributions
. 27
3.2
Rules of calculus for distributions
. 31
3.3
Distributions with compact support
. 36
3.4
Convolutions and coordinate changes
. 40
3.5
The calculation rules and the weak* topology on
3'. 46
Exercises for Chapter
3. 50
Part II Extensions and applications
4
Realizations and Sobolev spaces
.,. 57
4.1
Realizations of differential operators
. 57
4.2
Sobolev spaces
. 61
4.3
The one-dimensional case
. 68
4.4
Boundary value problems in higher dimensions
. 77
Exercises for Chapter
4. 86
x
Contents
5
Fourier transformation of distributions
. 05
5.1
Rapidly decreasing functions
. 95
5.2
Temperate distributions
.103
5.3
The Fourier transform on
З"
.105
5.4
Homogeneity
.110
5.5
Application to the Laplace operator
.114
5.6
Distributions associated with nonintegrable functions
.116
Exercises for Chapter
5.120
6
Applications to differential operators. The Sobolev theorem
123
6.1
Differential and pseudodifferential operators on R™
.123
6.2
Sobolev spaces of arbitrary real order. The Sobolev theorem
. 127
6.3
Dualities between Sobolev spaces. The Structure theorem
. 132
6.4
Regularity theory for elliptic differential equations
.138
Exercises for Chapter
6.144
Miscellaneous exercises (exam problems)
.147
Part III Pseudodifferential operators
7
Pseudodifferential operators on open sets
.163
7.1
Symbols and operators, mapping properties
. 163
7.2
Negligible operators
. 172
7.3
Composition rules
. 178
7.4
Elliptic pseudodifferential operators
. 183
7.5
Strongly elliptic operators, the
Gårding
inequality
. 189
Exercises for Chapter
7. 193
8
Pseudodifferential operators on manifolds, index of
elliptic operators
.195
8.1
Coordinate changes
.195
8.2
Operators on manifolds
.197
8.3
Fredholm
theory, the index
.208
Exercises for Chapter
8.215
Part IV Boundary value problems
9
Boundary value problems in a constant-coefficient case
. 219
9.1
Boundary maps for the half-space
.219
9.2
The Dirichlet problem for I
-
Δ
on the half-space
.228
9.3
The Neumann problem for I
—
Δ
on the half-space
.234
9.4
Other realizations of I
-
A
.236
9.5
Variable-coefficient cases, higher orders, systems
.
24(i
Exercises for Chapter
9.248
Contents
xi
10 Pseudodifferential
boundary operators
.251
10.1
The real formulation
.251
10.2
Fourier transform and Laguerre expansion of
<5^+
.266
10.3
The complex formulation
.275
10.4
Composition rules
.281
10.5
Continuity
.289
10.6
Elliptic ^dbo's
.296
Exercises for Chapter
10.300
11
Pseudodifferential methods for boundary value problems
. 305
11.1
The
Calderón
projector
.305
11.2
Application to boundary value problems
.317
11.3
The solution operator for the Dirichlet problem
.320
Exercises for Chapter
11.326
Part V Topics on Hubert space operators
12
Unbounded linear operators
.337
12.1
Unbounded operators in Banach spaces
.337
12.2
Unbounded operators in Hubert spaces
.340
12.3
Symmetric, selfadjoint and semibounded operators
.343
12.4
Operators associated with sesquilinear forms
.350
12.5
The
Friedrichs
extension
.359
12.6
More on variational operators
.361
Exercises for Chapter
12.364
13
Families of extensions
.373
13.1
A universal parametrization of extensions
.373
13.2
The symmetric case
.383
13.3
Consequences for resolvents
.393
13.4
Boundary triplets and M-functions
.397
Exercises for Chapter
13.402
14
Semigroups of operators
.405
14.1
Evolution equations
.405
14.2
Contraction semigroups in Banach spaces
.409
14.3
Contraction semigroups in Hubert spaces
.416
14.4
Applications
.419
Exercises for Chapter
14.421
A Some notation and prerequisites
.423
Exercises for Appendix A
.429
xii Contents
В
Topological
vector
spaces
. 431
B.I
Fréchet
spaces
. 431
В.
2
Inductive limits of
Fréchet
spaces
. 441
Exercises for Appendix
В
. 443
С
Function spaces on sets with smooth boundary
.447
Exercises for Appendix
G
.450
Bibliography
.451
Index
.457 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Grubb, Gerd 1939- |
| author_GND | (DE-588)136811175 |
| author_facet | Grubb, Gerd 1939- |
| author_role | aut |
| author_sort | Grubb, Gerd 1939- |
| author_variant | g g gg |
| building | Verbundindex |
| bvnumber | BV035187673 |
| callnumber-first | Q - Science |
| callnumber-label | QA324 |
| callnumber-raw | QA324 |
| callnumber-search | QA324 |
| callnumber-sort | QA 3324 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 990 SK 600 SK 620 |
| classification_tum | MAT 470f |
| ctrlnum | (OCoLC)258078542 (DE-599)DNB989571238 |
| dewey-full | 515.782 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.782 |
| dewey-search | 515.782 |
| dewey-sort | 3515.782 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035187673 |
| illustrated | Illustrated |
| index_date | 2024-07-02T23:00:27Z |
| indexdate | 2024-09-24T00:16:22Z |
| institution | BVB |
| isbn | 9780387848945 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016994351 |
| oclc_num | 258078542 |
| open_access_boolean | |
| owner | DE-384 DE-706 DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-83 DE-824 DE-11 DE-188 DE-91G DE-BY-TUM |
| owner_facet | DE-384 DE-706 DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-83 DE-824 DE-11 DE-188 DE-91G DE-BY-TUM |
| physical | XII, 461 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Grubb, Gerd 1939- Verfasser (DE-588)136811175 aut Distributions and operators Gerd Grubb New York, NY Springer 2009 XII, 461 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 252 Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Distribution Funktionalanalysis (DE-588)4070505-5 s Distributionstheorie (DE-588)4150254-1 s Pseudodifferentialoperator (DE-588)4047640-6 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-0-387-84895-2 Graduate texts in mathematics 252 (DE-604)BV000000067 252 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grubb, Gerd 1939- Distributions and operators Graduate texts in mathematics Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| subject_GND | (DE-588)4150254-1 (DE-588)4070505-5 (DE-588)4047640-6 (DE-588)4123623-3 |
| title | Distributions and operators |
| title_auth | Distributions and operators |
| title_exact_search | Distributions and operators |
| title_exact_search_txtP | Distributions and operators |
| title_full | Distributions and operators Gerd Grubb |
| title_fullStr | Distributions and operators Gerd Grubb |
| title_full_unstemmed | Distributions and operators Gerd Grubb |
| title_short | Distributions and operators |
| title_sort | distributions and operators |
| topic | Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| topic_facet | Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie Distribution Funktionalanalysis Pseudodifferentialoperator Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT grubbgerd distributionsandoperators |