Recent Advances in Differential Equations and Mathematical Physics
About this Title
Nikolai Chernov, Yulia Karpeshina, Ian W. Knowles, Roger T. Lewis and Rudi Weikard, Editors
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.
Graduate students and research mathematicians interested in quantum theory, spectral theory of Schroedinger operators, inverse problems, and inverse algorithms.
Table of Contents
- Michael Aizenman, Robert Sims and Simone Warzel – Fluctuation based proof of the stability of ac spectra of random operators on tree graphs [MR 2259096]
- Tuncay Aktosun and Ricardo Weder – The Borg-Marchenko theorem with a continuous spectrum [MR 2259097]
- M. H. Annaby, G. Freiling and I. A. Soliman – Sampling theorems associated with differential operators iterated from lower order ones [MR 2259098]
- Wolfgang Arendt, Gisèle Ruiz Goldstein and Jerome A. Goldstein – Outgrowths of Hardy’s inequality [MR 2259099]
- Alexander A. Balinsky and Alexey E. Tyukov – On Hardy type inequalities [MR 2259100]
- Rafael D. Benguria – A nonlinear fourth-order minimization problem [MR 2259101]
- B. M. Brown, M. Jais and P. C. Kalmbach – A variational approach to inverse problems for anisotropic systems [MR 2259102]
- Steve Clark and Fritz Gesztesy – On self-adjoint and $J$-self-adjoint Dirac-type operators: a case study [MR 2259103]
- Pavel Exner – Necklaces with interacting beads: isoperimetric problems [MR 2259104]
- Colin Fox, Vladimir Oleinik and Boris Pavlov – A Dirichlet-to-Neumann map approach to resonance gaps and bands of periodic networks [MR 2259105]
- G. Gallavotti – Resonances and summation of divergent series [MR 2259106]
- George A. Hagedorn and Alain Joye – Recent results on non-adiabatic transitions in quantum mechanics [MR 2259107]
- Rainer Hempel – Schrödinger operators with strong magnetic fields of compact support [MR 2259108]
- Don Hinton and Maeve L. McCarthy – Optimization of the minimum eigenvalue for a class of second order differential operators [MR 2259109]
- Richard Lavine – Time of arrival in quantum mechanics and the quantum Zeno effect [MR 2259110]
- Elliott H. Lieb, Robert Seiringer and Jan Philip Solovej – Ground-state energy of a dilute Fermi gas [MR 2259111]
- Leonid Pestov and Gunther Uhlmann – The scattering relation and the Dirichlet-to-Neumann map [MR 2259112]
- Norbert Röhrl – Recovering boundary conditions in inverse Sturm-Liouville problems [MR 2259113]
- Alexei Rybkin – Preservation of the absolutely continuous spectrum: some extensions of a result by Molchanov-Novitskii-Vainberg [MR 2259114]
- Vadim Tkachenko – Expansions associated with 1d periodic differential operators of order 4 [MR 2259115]
- Lloyd N. Trefethen and Timo Betcke – Computed eigenmodes of planar regions [MR 2259116]
- András Vasy – Geometric optics and the wave equation on manifolds with corners [MR 2259117]