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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
Layer Potential Techniques in Spectral Analysis
Hardcover ISBN:  978-0-8218-4784-8
Product Code:  SURV/153
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1380-4
Product Code:  SURV/153.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4784-8
eBook: ISBN:  978-1-4704-1380-4
Product Code:  SURV/153.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Layer Potential Techniques in Spectral Analysis
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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
Hardcover ISBN:  978-0-8218-4784-8
Product Code:  SURV/153
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1380-4
Product Code:  SURV/153.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4784-8
eBook ISBN:  978-1-4704-1380-4
Product Code:  SURV/153.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • 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.

    Readership

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

  • Table of Contents
     
     
    • 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 publishers of book reviews
    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.

Readership

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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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