Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 111 S. |
Internformat
MARC
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| 100 | 1 | |a Noll, André |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory |c vorgelegt von André Noll |
| 264 | 1 | |c 2000 | |
| 300 | |a VI, 111 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Clausthal, Techn. Univ., Diss., 2000 | ||
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| 650 | 0 | 7 | |a Kapazität |g Mathematik |0 (DE-588)4163239-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Eigenwert |0 (DE-588)4151200-5 |2 gnd |9 rswk-swf |
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| 689 | 1 | 2 | |a Eigenwert |0 (DE-588)4151200-5 |D s |
| 689 | 1 | 3 | |a Störungstheorie |0 (DE-588)4128420-3 |D s |
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Datensatz im Suchindex
| _version_ | 1807864971356274688 |
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| adam_text |
CONTENTS
1
THE
SIGNIFICANCE
OF
THE
BOTTOM
EIGENVALUE
IN
MATHEMATICAL
PHYSICS
1
1.1
PRELIMINARIES
ON
THE
DIRICHLET
LAPLACIAN
ON
A
BOUNDED
DOMAIN
2
1.2
INTERPRETATION
OF
THE
BOTTOM
EIGENVALUE
FOR
THE
HEAT
EQUATION
3
1.3
THE
SIGNIFICANCE
OF
THE
BOTTOM
EIGENVALUE
IN
QUANTUM
MECHANICS
4
1.4
DOMAIN
PERTURBATIONS
IN
MATHEMATICAL
PHYSICS
.
6
2
DEFINING
OF
OPERATORS
BY
QUADRATIC
FORMS
7
2.1
THE
ONE-TO-ONE
CORRESPONDENCE
BETWEEN
QUADRATIC
FORMS
AND
SELF-ADJOINT
OPERATORS
.
7
2.2
ADVANTAGES
OF
THE
QUADRATIC
FORM
TECHNIQUE
.
10
3
DOMAIN
PERTURBATIONS
12
3.1
THE
L
2
-CASE
.
13
3.2
THE
GENERAL
HILBERT
SPACE
CASE
.
15
3.3
DEFINING
DOMAIN
PERTURBATIONS
BY
MEANS
OF
THE
ASSOCIATED
STOCHASTIC
PROCESS
.
21
3.4
PRELIMINARY
REMARKS
ON
THE
SPECTRUM
OF
THE
PERTURBED
OPERATOR
23
4
SEVERAL
APPROACHES
TO
CAPACITY
24
4.1
DEFINITION
OF
THE
ELECTROSTATIC
CAPACITY
.
25
4.2
THE
CAPACITY
OF
A
REGULAR
DIRICHLET
FORM
.
27
4.3
CAPACITY
IN
GENERAL
HILBERT
SPACES
.
31
4.4
OTHER
CAPACITIES
.
35
4.4.1
THE
CAPACITY
OF
A
NON-REGULAR,
NON-SYMMETRIC
DIRICHLET
FORM
.
35
4.4.2
CAPACITIES
ON
IC*
.
37
5
CAPACITARY
ESTIMATES
FOR
DOMAIN
PERTURBATIONS
39
5.1
UPPER
BOUNDS
FOR
THE
BOTTOM
EIGENVALUE
.
40
5.1.1
THE
GROUND-STATE
TRANSFORMATION
.
42
5.1.2
AN
UPPER
BOUND
IN
THE
GENERAL
HILBERT
SPACE
SETTING
.
46
5.2
LOWER
BOUNDS
FOR
THE
BOTTOM
EIGENVALUE
.
50
5.3
HIGHER
EIGENVALUES
.
55
5.4
ADDITIVE
PERTURBATIONS
.
63
5.5
OPERATORS
WITH
SPECTRAL
BOUND
OF
ARBITRARY
TYPE
.
65
6
APPLICATIONS
TO
DIFFERENTIAL
OPERATORS
OF
ARBITRARY
ORDER
67
6.1
CAPACITARY
EIGENVALUE
ESTIMATES
FOR
DOMAIN
PERTURBATIONS
OF
DIFFERENTIAL
OPERATORS
.
68
6.2
STUMMEL
CLASS
PERTURBATIONS
.
72
7
SCALING
METHODS
74
7.1
THE
SCALING
PROPERTY
OF
THE
CLASSICAL
ZERO-ORDER
CAPACITY
IN
IT*
75
7.2
THE
ZERO-ORDER
CAPACITY
IN
THE
GENERAL
HILBERT
SPACE
SETTING
.
.
77
7.3
SCALING
INVARIANCE
OF
EIGENVALUE
ESTIMATES
.
81
8
OPEN
PROBLEMS
85
A
APPENDIX
88
A.L
THE
MINIMAX
PRINCIPLE
.
88
A.
2
SOBOLEV
SPACES
OF
FRACTIONAL
ORDER
AND
THE
ELLIPTIC
REGULARITY
THEOREM
.
88
A.3
MARKOV
PROCESSES
AND
HUNT
PROCESSES
.
90
A.4
BASICS
ON
REGULAR
DIRICHLET
FORMS
.
95
V
REFERENCES
103
INDEX
109
LIST
OF
FIGURES
1
DOMAIN
PERTURBATIONS
.
6
2
THE
FUNCTION
V
N
FOR
N
=
5
AND
XJ
=
J
.
11
3
A
DOMAIN
WITH
AJ
=
63
VI |
| any_adam_object | 1 |
| author | Noll, André |
| author_facet | Noll, André |
| author_role | aut |
| author_sort | Noll, André |
| author_variant | a n an |
| building | Verbundindex |
| bvnumber | BV013157924 |
| classification_tum | MAT 474d MAT 463d |
| ctrlnum | (OCoLC)247617203 (DE-599)BVBBV013157924 |
| discipline | Mathematik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV013157924 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-20T00:39:49Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008965199 |
| oclc_num | 247617203 |
| open_access_boolean | |
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| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-83 DE-188 |
| physical | VI, 111 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| record_format | marc |
| spelling | Noll, André Verfasser aut Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory vorgelegt von André Noll 2000 VI, 111 S. txt rdacontent n rdamedia nc rdacarrier Clausthal, Techn. Univ., Diss., 2000 Störungstheorie (DE-588)4128420-3 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Selbstadjungierter Operator (DE-588)4180810-1 gnd rswk-swf Kapazität Mathematik (DE-588)4163239-4 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Störungstheorie (DE-588)4128420-3 s Hilbert-Raum (DE-588)4159850-7 s DE-604 Selbstadjungierter Operator (DE-588)4180810-1 s Eigenwert (DE-588)4151200-5 s Kapazität Mathematik (DE-588)4163239-4 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008965199&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noll, André Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory Störungstheorie (DE-588)4128420-3 gnd Hilbert-Raum (DE-588)4159850-7 gnd Selbstadjungierter Operator (DE-588)4180810-1 gnd Kapazität Mathematik (DE-588)4163239-4 gnd Eigenwert (DE-588)4151200-5 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4159850-7 (DE-588)4180810-1 (DE-588)4163239-4 (DE-588)4151200-5 (DE-588)4113937-9 |
| title | Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory |
| title_auth | Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory |
| title_exact_search | Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory |
| title_full | Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory vorgelegt von André Noll |
| title_fullStr | Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory vorgelegt von André Noll |
| title_full_unstemmed | Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory vorgelegt von André Noll |
| title_short | Domain perturbations and capacity in general Hilbert spaces and applications to spectral theory |
| title_sort | domain perturbations and capacity in general hilbert spaces and applications to spectral theory |
| topic | Störungstheorie (DE-588)4128420-3 gnd Hilbert-Raum (DE-588)4159850-7 gnd Selbstadjungierter Operator (DE-588)4180810-1 gnd Kapazität Mathematik (DE-588)4163239-4 gnd Eigenwert (DE-588)4151200-5 gnd |
| topic_facet | Störungstheorie Hilbert-Raum Selbstadjungierter Operator Kapazität Mathematik Eigenwert Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008965199&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nollandre domainperturbationsandcapacityingeneralhilbertspacesandapplicationstospectraltheory |