**Contemporary Mathematics**

Volume: 412;
2006;
333 pp;
Softcover

MSC: Primary 34; 35; 81;

Print ISBN: 978-0-8218-3840-2

Product Code: CONM/412

List Price: $97.00

Individual Member Price: $77.60

**Electronic ISBN: 978-0-8218-8085-2
Product Code: CONM/412.E**

List Price: $97.00

Individual Member Price: $77.60

# Recent Advances in Differential Equations and Mathematical Physics

Share this page *Edited by *
*Nikolai Chernov; Yulia Karpeshina; Ian W. Knowles; Roger T. Lewis; Rudi Weikard*

This book brings together both new material and recent surveys on some topics in differential equations that are either directly relevant to, or closely associated with, mathematical physics.

Its topics include asymptotic formulas for the ground-state energy of fermionic gas, renormalization ideas in quantum field theory from perturbations of the free Hamiltonian on the circle, \(J\)-selfadjoint Dirac operators, spectral theory of Schrödinger operators, inverse problems, isoperimetric inequalities in quantum mechanics, Hardy inequalities, and non-adiabatic transitions.

Excellent survey articles on Dirichlet-Neumann inverse problems on manifolds (by Uhlmann), numerical investigations associated with Laplacian eigenvalues on planar regions (by Trefethen), Snell's law and propagation of singularities in the wave equation (by Vasy), and random operators on tree graphs (by Aizenmann) make this book interesting and valuable for graduate students, young mathematicians, and physicists alike.

#### Table of Contents

# Table of Contents

## Recent Advances in Differential Equations and Mathematical Physics

- Contents v6 free
- Preface vii8 free
- List of Plenary Speakers ix10 free
- List of Participants xi12 free
- Fluctuation based proof of the stability of ac spectra of random operators on tree graphs 120 free
- The Borg-Marchenko Theorem with a Continuous Spectrum 1534
- Sampling Theorems Associated With Differential Operators Iterated From Lower Order Ones 3150
- Outgrowths of Hardy's Inequality 5170
- On Hardy type inequalities 6988
- A nonlinear fourth–order minimization problem 7998
- A variational approach to inverse problems for anisotropic systems 87106
- On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case Study 103122
- Necklaces with interacting beads: isoperimetric problems 141160
- A Dirichlet-to-Neumann map approach to resonance gaps and bands of periodic networks 151170
- Resonances and summation of divergent series 171190
- Recent Results on Non–Adiabatic Transitions in Quantum Mechanics 183202
- Schrödinger Operators with Strong Magnetic Fields of Compact Support 199218
- Optimization of the minimum eigenvalue for a class of second order differential operators 207226
- Time of Arrival in Quantum Mechanics and the Quantum Zeno Effect 227246
- Ground-State Energy of a Dilute Fermi Gas 239258
- The scattering relation and the Dirichlet-to-Neumann map 249268
- Recovering boundary conditions in inverse Sturm-Liouville problems 263282
- Preservation of the absolutely continuous spectrum: some extensions of a result by Molchanov-Novitskii-Vainberg 271290
- Expansions associated with 1d periodic differential operators of order 4 283302
- Computed eigenmodes of planar regions 297316
- Geometric optics and the wave equation on manifolds with corners 315334

#### Readership

Graduate students and research mathematicians interested in quantum theory, spectral theory of Schroedinger operators, inverse problems, and inverse algorithms.