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 𝑘 minimal spectral 𝑘-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 𝒪^{#}.

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^{𝕕} 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 𝑃_{𝐵} and 𝑇_{𝐵}

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