Electronic ISBN:  9780821880852 
Product Code:  CONM/412.E 
List Price:  $97.00 
MAA Member Price:  $87.30 
AMS Member Price:  $77.60 

Book DetailsContemporary MathematicsVolume: 412; 2006; 333 ppMSC: Primary 34; 35; 81;
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 groundstate 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 nonadiabatic transitions.
Excellent survey articles on DirichletNeumann 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.ReadershipGraduate students and research mathematicians interested in quantum theory, spectral theory of Schroedinger operators, inverse problems, and inverse algorithms.

Table of Contents

Articles

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 BorgMarchenko 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 fourthorder 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 selfadjoint and $J$selfadjoint Diractype operators: a case study [ MR 2259103 ]

Pavel Exner  Necklaces with interacting beads: isoperimetric problems [ MR 2259104 ]

Colin Fox, Vladimir Oleinik and Boris Pavlov  A DirichlettoNeumann 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 nonadiabatic 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  Groundstate energy of a dilute Fermi gas [ MR 2259111 ]

Leonid Pestov and Gunther Uhlmann  The scattering relation and the DirichlettoNeumann map [ MR 2259112 ]

Norbert Röhrl  Recovering boundary conditions in inverse SturmLiouville problems [ MR 2259113 ]

Alexei Rybkin  Preservation of the absolutely continuous spectrum: some extensions of a result by MolchanovNovitskiiVainberg [ 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 ]


Additional Material

Request Review Copy

Get Permissions
 Book Details
 Table of Contents
 Additional Material

 Request Review Copy
 Get Permissions
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 groundstate 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 nonadiabatic transitions.
Excellent survey articles on DirichletNeumann 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.

Articles

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 BorgMarchenko 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 fourthorder 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 selfadjoint and $J$selfadjoint Diractype operators: a case study [ MR 2259103 ]

Pavel Exner  Necklaces with interacting beads: isoperimetric problems [ MR 2259104 ]

Colin Fox, Vladimir Oleinik and Boris Pavlov  A DirichlettoNeumann 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 nonadiabatic 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  Groundstate energy of a dilute Fermi gas [ MR 2259111 ]

Leonid Pestov and Gunther Uhlmann  The scattering relation and the DirichlettoNeumann map [ MR 2259112 ]

Norbert Röhrl  Recovering boundary conditions in inverse SturmLiouville problems [ MR 2259113 ]

Alexei Rybkin  Preservation of the absolutely continuous spectrum: some extensions of a result by MolchanovNovitskiiVainberg [ 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 ]