Layer potential techniques in spectral analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2009
|
| Series: | Mathematical surveys and monographs
153 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 191-200) and index |
| Physical Description: | vi, 202 p. ill. 26 cm |
| ISBN: | 9780821847848 0821847848 |
Staff View
MARC
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| 020 | |a 9780821847848 |c alk. paper |9 978-0-8218-4784-8 | ||
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| 100 | 1 | |a Ammari, Habib |d 1969- |e Verfasser |0 (DE-588)129355119 |4 aut | |
| 245 | 1 | 0 | |a Layer potential techniques in spectral analysis |c Habib Ammari ; Hyeonbae Kang ; Hyundae Lee |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2009 | |
| 300 | |a vi, 202 p. |b ill. |c 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 153 | |
| 500 | |a Includes bibliographical references (p. 191-200) and index | ||
| 650 | 4 | |a Differential equations, Elliptic | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 4 | |a Composite materials |x Spectra | |
| 650 | 4 | |a Eigenvalues | |
| 650 | 4 | |a Boundary element methods | |
| 650 | 4 | |a Photonic crystals | |
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |D s |
| 689 | 0 | 1 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kang, Hyeonbae |d 1960- |e Sonstige |0 (DE-588)1029525706 |4 oth | |
| 700 | 1 | |a Lee, Hyundae |d 1976- |e Sonstige |0 (DE-588)138145474 |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1380-4 |
| 830 | 0 | |a Mathematical surveys and monographs |v 153 |w (DE-604)BV000018014 |9 153 | |
| 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=018659411&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018659411 | ||
Record in the Search Index
| _version_ | 1804140745868705792 |
|---|---|
| adam_text | Contents
Introduction
Part
1.
Gohberg and Sigal Theory
5
Chapter
1.
Generalized Argument Principle and
Rouché s
Theorem
7
1.1.
Definitions and Preliminaries
8
1.2.
Factorization of Operators
11
1.3.
Main Results of the Gohberg and Sigal Theory
12
1.4.
Concluding Remarks
16
Part
2.
Eigenvalue Perturbation Problems and Applications
17
Chapter
2.
Layer Potentials
19
2.1.
Sobolev Spaces
19
2.2.
Layer Potentials for the Laplace Equation
20
2.3.
Layer Potentials for the Helmholtz Equation
22
2.4.
Integral Representation of Solutions to the
Lamé
System
28
2.5.
Concluding Remarks
33
Chapter
3.
Eigenvalue Perturbations of the Laplacian
35
3.1.
Eigenvalue Perturbations Due to Small Grounded Inclusions
35
3.2.
Eigenvalue Perturbations Due to Conductivity Inclusions
47
3.3.
Eigenvalue Perturbations Due to Shape Deformations
54
3.4.
Splitting of Multiple Eigenvalues
60
3.5.
Reconstruction of Inclusions
61
3.6.
Reconstruction of Shape Deformations
68
3.7.
Concluding Remarks
74
Chapter
4.
Vibration Testing for Detecting Internal Corrosion
77
4.1.
Introduction
77
4.2.
Formal Derivations
77
4.3.
Reconstruction Method
79
4.4.
Numerical Results
81
4.5.
Justification of the Asymptotic Expansion
84
4.6.
Concluding Remarks
89
Chapter
5.
Perturbations of Scattering Frequencies of Resonators with
Narrow Slits and Slots
91
5.1.
Introduction
91
5.2.
Perturbations of Scattering Frequencies Due to Narrow Slits
91
5.3.
Perturbations of Scattering Frequencies of a Helmholtz Resonator
99
vi
CONTENTS
5.4.
Concluding Remarks
101
Chapter
6.
Eigenvalue Perturbations of the
Lamé
System
103
6.1.
Introduction
103
6.2.
Hard Inclusion Case
104
6.3.
Transmission Problem
108
6.4.
Eigenvalue Perturbations Due to Shape Deformations
115
6.5.
Reconstruction of Inclusions
115
6.6.
Concluding Remarks
117
Part
3.
Photonic and Phononic Band Gaps and Optimal Design
119
Chapter
7.
Floquet Transform, Spectra of Periodic Elliptic Operators, and
Quasi-Periodic Layer Potentials
121
7.1.
Floquet Transform
121
7.2.
Structure of Spectra of Periodic Elliptic Operators
122
7.3.
Quasi-Periodic Layer Potentials for the Helmholtz Equation
123
7.4.
Quasi-Periodic Layer Potentials for the
Lamé
System
126
7.5.
Computations of Periodic Green s Functions
128
7.6.
Muller s Method
131
7.7.
Concluding Remarks
132
Chapter
8.
Photonic Band Gaps
133
8.1.
Introduction
133
8.2.
Boundary Integral Formulation
134
8.3.
Sensitivity Analysis with Respect to the Index Ratio
137
8.4.
Photonic Band Gap Opening
146
8.5.
Sensitivity Analysis with Respect to Small Perturbations in the
Geometry of the Holes
146
8.6.
Proof of the Representation Formula
147
8.7.
Characterization of the Eigenvalues of
Δ
149
8.8.
Concluding Remarks
150
Chapter
9.
Phononic Band Gaps
153
9.1.
Introduction
153
9.2.
Asymptotic Behavior of Phononic Band Gaps
155
9.3.
Criterion for Gap Opening
171
9.4.
Gap Opening Criterion When Densities Are Different
175
9.5.
Concluding Remarks
178
Chapter
10.
Optimal Design Problems
179
10.1.
Introduction
179
10.2.
The Acoustic Drum Problem
179
10.3.
An Optimal Control Approach in Shape Optimization
184
10.4.
Maximizing Band Gaps in Photonic Crystals
186
10.5.
Approximate Optimal Design Problems for Photonic Crystals
188
10.6.
Concluding Remarks
189
Bibliography
191
Index
201
|
| any_adam_object | 1 |
| author | Ammari, Habib 1969- |
| author_GND | (DE-588)129355119 (DE-588)1029525706 (DE-588)138145474 |
| author_facet | Ammari, Habib 1969- |
| author_role | aut |
| author_sort | Ammari, Habib 1969- |
| author_variant | h a ha |
| building | Verbundindex |
| bvnumber | BV035800261 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA377 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 SK 620 |
| ctrlnum | (OCoLC)271812165 (DE-599)BVBBV035800261 |
| dewey-full | 515/.3533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.3533 |
| dewey-search | 515/.3533 |
| dewey-sort | 3515 43533 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035800261 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:52Z |
| institution | BVB |
| isbn | 9780821847848 0821847848 |
| language | English |
| lccn | 2008048317 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018659411 |
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| owner | DE-355 DE-BY-UBR DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-20 |
| physical | vi, 202 p. ill. 26 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Ammari, Habib 1969- Verfasser (DE-588)129355119 aut Layer potential techniques in spectral analysis Habib Ammari ; Hyeonbae Kang ; Hyundae Lee Providence, R.I. American Mathematical Society 2009 vi, 202 p. ill. 26 cm txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 153 Includes bibliographical references (p. 191-200) and index Differential equations, Elliptic Spectral theory (Mathematics) Composite materials Spectra Eigenvalues Boundary element methods Photonic crystals Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Spektraltheorie (DE-588)4116561-5 s DE-604 Kang, Hyeonbae 1960- Sonstige (DE-588)1029525706 oth Lee, Hyundae 1976- Sonstige (DE-588)138145474 oth Erscheint auch als Online-Ausgabe 978-1-4704-1380-4 Mathematical surveys and monographs 153 (DE-604)BV000018014 153 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018659411&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ammari, Habib 1969- Layer potential techniques in spectral analysis Mathematical surveys and monographs Differential equations, Elliptic Spectral theory (Mathematics) Composite materials Spectra Eigenvalues Boundary element methods Photonic crystals Elliptische Differentialgleichung (DE-588)4014485-9 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4116561-5 |
| title | Layer potential techniques in spectral analysis |
| title_auth | Layer potential techniques in spectral analysis |
| title_exact_search | Layer potential techniques in spectral analysis |
| title_full | Layer potential techniques in spectral analysis Habib Ammari ; Hyeonbae Kang ; Hyundae Lee |
| title_fullStr | Layer potential techniques in spectral analysis Habib Ammari ; Hyeonbae Kang ; Hyundae Lee |
| title_full_unstemmed | Layer potential techniques in spectral analysis Habib Ammari ; Hyeonbae Kang ; Hyundae Lee |
| title_short | Layer potential techniques in spectral analysis |
| title_sort | layer potential techniques in spectral analysis |
| topic | Differential equations, Elliptic Spectral theory (Mathematics) Composite materials Spectra Eigenvalues Boundary element methods Photonic crystals Elliptische Differentialgleichung (DE-588)4014485-9 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Differential equations, Elliptic Spectral theory (Mathematics) Composite materials Spectra Eigenvalues Boundary element methods Photonic crystals Elliptische Differentialgleichung Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018659411&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT ammarihabib layerpotentialtechniquesinspectralanalysis AT kanghyeonbae layerpotentialtechniquesinspectralanalysis AT leehyundae layerpotentialtechniquesinspectralanalysis |