Recent Advances in Differential Equations and Mathematical Physics
Published on 1. July 2006
Book
Paperback/Softback
333 pages
978-0-8218-3840-2 (ISBN)
Description
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, $J$-self adjoint Dirac operators, spectral theory of Schrodinger 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.
More details
Series
Edition
illustrated Edition
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Illustrations
Illustrations
Weight
617 gr
ISBN-13
978-0-8218-3840-2 (9780821838402)
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Schweitzer Classification
Content
Fluctuation based proof of the stability of ac spectra of random operators on tree graphs by M. Aizenman, R. Sims, and S. Warzel The Borg-Marchenko theorem with a continuous spectrum by T. Aktosun and R. Weder Sampling theorems associated with differential operators iterated from lower order ones by M. H. Annaby, G. Freiling, and I. A. Soliman Outgrowths of Hardy's inequality by W. Arendt, G. R. Goldstein, and J. A. Goldstein On Hardy type inequalities by A. A. Balinsky and A. E. Tyukov A nonlinear fourth-order minimization problem by R. D. Benguria A variational approach to inverse problems for anistropic systems by B. M. Brown, M. Jais, and P. C. Kalmbach On self-adjoint and $J$-self-adjoint Dirac type operators: A case study by S. Clark and F. Gesztesy Necklaces with interacting beads: Isoperimetric problems by P. Exner A Dirichlet-to-Neumann map approach to resonance gaps and bands of periodic networks by C. Fox, V. Oleinik, and B. Pavlov Resonances and summation of divergent series by G. Gallavotti Recent results on non-adiabatic transitions in quantum mechanics by G. A. Hagedorn and A. Joye Schrodinger operators with strong magnetic fields of compact support by R. Hempel Optimization of the minimum eigenvalue for a class of second order differential operators by D. Hinton and M. L. McCarthy Time of arrival in quantum mechanics and the quantum zeno effect by R. Lavine Ground-state energy of a dilute Fermi gas by E. H. Lieb, R. Seiringer, and J. P. Solovej The scattering relation and the Dirichlet-to-Neumann map by L. Pestov and G. Uhlmann Recovering boundary conditions in inverse Sturm-Liouville problems by N. Rohrl Preservation of the absolutely continuous spectrum: Some extensions of a result by Molchanov-Novitskii-Vainberg by A. Rybkin Expansions associated with 1d periodic differential operators of order 4 by V. Tkachenko Computed eigenmodes of planar regions by L. N. Trefethen and T. Betcke Geometric optics and the wave equation on manifolds with corners by A. Vasy.