An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
Layer Potential Techniques in Spectral Analysis

Habib Ammari Ecole Polytechnique, Palaiseau, France
Hyeonbae Kang Inha University, Incheon, South Korea
Hyundae Lee Inha University, Incheon, South Korea
Available Formats:
Hardcover ISBN: 978-0-8218-4784-8
Product Code: SURV/153
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Electronic ISBN: 978-1-4704-1380-4 Product Code: SURV/153.E List Price:$73.00
MAA Member Price: $65.70 AMS Member Price:$58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00 MAA Member Price:$105.30
AMS Member Price: $93.60 Click above image for expanded view Layer Potential Techniques in Spectral Analysis Habib Ammari Ecole Polytechnique, Palaiseau, France Hyeonbae Kang Inha University, Incheon, South Korea Hyundae Lee Inha University, Incheon, South Korea Available Formats:  Hardcover ISBN: 978-0-8218-4784-8 Product Code: SURV/153  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
 Electronic ISBN: 978-1-4704-1380-4 Product Code: SURV/153.E
 List Price: $73.00 MAA Member Price:$65.70 AMS Member Price: $58.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$93.60
• Book Details

Mathematical Surveys and Monographs
Volume: 1532009; 202 pp
MSC: Primary 47; 31; 34; 35; 45; 30;

Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single- and double-layer potentials to treat classical boundary value problems.

The aim of this book is to give a self-contained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals. Throughout this book, it is shown how powerful the layer potentials techniques are for solving not only boundary value problems but also eigenvalue problems if they are combined with the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. The general approach in this book is developed in detail for eigenvalue problems for the Laplacian and the Lamé system in the following two situations: one under variation of domains or boundary conditions and the other due to the presence of inclusions.

The book will be of interest to researchers and graduate students working in the fields of partial differential equations, integral equations, and inverse problems. Researchers in engineering and physics may also find this book helpful.

Graduate students and research mathematicians interested in PDE's, integral equations, and spectral analysis.

• Chapters
• Introduction
• Gohberg-Sigal theory
• 1. Generalized argument principle and Rouché’s theorem
• Eigenvalue perturbation problems and applications
• 2. Layer potentials
• 3. Eigenvalue perturbations of the Laplacian
• 4. Vibration testing for detecting internal corrosion
• 5. Perturbations of scattering frequencies of resonators with narrow slits and slots
• 6. Eigenvalue perturbations of the Lamé system
• Photonic and phononic band gaps and optimal design
• 7. Floquet transform, spectra of periodic elliptic operators, and quasi-periodic layer potentials
• 8. Photonic band gaps
• 9. Phononic band gaps
• 10. Optimal design problems

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1532009; 202 pp
MSC: Primary 47; 31; 34; 35; 45; 30;

Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single- and double-layer potentials to treat classical boundary value problems.

The aim of this book is to give a self-contained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals. Throughout this book, it is shown how powerful the layer potentials techniques are for solving not only boundary value problems but also eigenvalue problems if they are combined with the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. The general approach in this book is developed in detail for eigenvalue problems for the Laplacian and the Lamé system in the following two situations: one under variation of domains or boundary conditions and the other due to the presence of inclusions.

The book will be of interest to researchers and graduate students working in the fields of partial differential equations, integral equations, and inverse problems. Researchers in engineering and physics may also find this book helpful.

Graduate students and research mathematicians interested in PDE's, integral equations, and spectral analysis.

• Chapters
• Introduction
• Gohberg-Sigal theory
• 1. Generalized argument principle and Rouché’s theorem
• Eigenvalue perturbation problems and applications
• 2. Layer potentials
• 3. Eigenvalue perturbations of the Laplacian
• 4. Vibration testing for detecting internal corrosion
• 5. Perturbations of scattering frequencies of resonators with narrow slits and slots
• 6. Eigenvalue perturbations of the Lamé system
• Photonic and phononic band gaps and optimal design
• 7. Floquet transform, spectra of periodic elliptic operators, and quasi-periodic layer potentials
• 8. Photonic band gaps
• 9. Phononic band gaps
• 10. Optimal design problems
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.