Spectral Theory and Partial Differential Equations.

Cover -- Title page -- Contents -- Preface -- Algebras in reconstruction of manifolds -- 0. Introduction -- 1. Setup -- 2. Algebras -- 3. Eikonal algebra in acoustics -- 4. Eikonal algebra in electrodynamics -- References -- Spectral theory of a mathematical model in quantum field theory for any spin -- 1. Introduction -- 2. Free causal fields for massive and massless particles of any spin -- 3. Definition of the model -- 4. A self-adjoint Hamiltonian -- 5. Main results -- 6. Spectral gap for cutoff operators -- 7. Proof of theorem 5.2 -- 8. Proof of theorem 5.3 -- Acknowledgements -- References -- A review on large minimal spectral -partitions and Pleijel's Theorem -- 1. Introduction -- 2. A reminder on minimal spectral partitions -- 3. Pleijel's Theorem revisited -- 4. Improving the use of the Faber-Krahn Inequality -- 5. Considerations around rectangles -- 6. Looking for a class ^{#}. -- 7. Pleijel's Theorem for Aharonov-Bohm operators and application to minimal partitions -- References -- Increasing stability for near field from the scattering amplitude -- 1. Introduction -- 2. Some bounds of Hankel functions -- 3. Proof of main results -- 4. Application to linearized inverse obstacle scattering -- 5. Conclusion -- References -- Inverse scattering on multi-dimensional asymptotically hyperbolic orbifolds -- 1. Introduction -- 2. 3-dimensional hyperbolic orbifolds -- 3. Helmholtz equation and the S-matrix -- 4. Inverse scattering from cusp -- 5. Orbifold isomorphism -- References -- Error estimates of the Bloch band-based Gaussian beam superposition for the Schrödinger equation -- 1. Introduction -- 2. Set-up and main results -- 3. Construction -- 4. Initial error-proof of Theorem 2.1. -- 5. Evolution error-proof of Theorem 2.2 -- 6. Extensions -- Acknowledgments -- References.

On random weighted Sobolev inequalities on ℝ^{ } and applications -- 1. Introduction -- 2. Spectral estimates and harmonic Sobolev spaces -- 3. Probabilistic weighted estimates for frequency localized functions -- 4. Hermite functions estimates -- 5. Application to quantum ergodicity -- 6. Application to supercritical nonlinear Schrödinger equations -- Appendix A. Proof of Theorem 3.2 -- Appendix B. Proof of Theorem 3.5 -- References -- Calderón problem for Maxwell's equations in the waveguide -- 1. Introduction and main results -- 2. Step 1: Reduction of the Maxwell's equations to the decoupled system of elliptic equations -- 3. Step 2: Construction of the operators _{ } and _{ } -- 4. Step 3: Construction of complex geometric optics solutions -- 5. Step 4: Asymptotics -- 6. Step 5: End of the proof -- References -- Gaussian beams on Zoll manifolds and maximally degenerate Laplacians -- 1. Introduction -- 2. Jacobi fields and Poincaré map on a Zoll manifold -- 3. Gaussiam beam quasi-modes -- 4. Quantum Birkhoff normal form construction -- 5. Maximally degenerate Zoll case -- 6. Explicit formulae on Zoll surfaces -- 7. Final Remarks -- References -- Back Cover.

This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17-21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday. Papers in this volume cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.