Spectral invariants of the magnetic Dirichlet-to-Neumann map on Riemannian manifolds

DOI10.1063/5.0088549zbMath1512.35419arXiv2108.07611OpenAlexW4366571905MaRDI QIDQ6042738

Genqian Liu, Xiaoming Tan

Publication date: 4 May 2023

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.07611

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Inverse problems for PDEs (35R30) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10) Pseudodifferential and Fourier integral operators on manifolds (58J40)

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Cites Work

• A global uniqueness theorem for an inverse boundary value problem
• The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues on Riemannian manifolds
• Uniqueness of the self-adjoint extension of singular elliptic differential operators
• Sloshing frequencies
• Limiting Carleman weights and anisotropic inverse problems
• Spectral methods in surface superconductivity
• Partial differential equations. III: Nonlinear equations.
• Inverse scattering for the magnetic Schrödinger operator
• Stability estimate for an inverse problem for the magnetic Schrödinger equation from the Dirichlet-to-Neumann map
• Functional calculus of pseudo-differential boundary problems
• Some asymptotic formulas for elliptic pseudodifferential operators
• The spectrum of positive elliptic operators and periodic bicharacteristics
• The spectral geometry of a Riemannian manifold
• Essential self-adjointness of the Schrödinger operator with magnetic vector potential
• On essential self-adjointness for singular elliptic differential operators
• Schrödinger operators with magnetic fields. I: General interactions
• Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometries
• Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field
• Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems
• Geometric invariants of spectrum of the Navier-Lamé operator
• The geometric invariants for the spectrum of the Stokes operator
• Spectral invariants of the perturbed polyharmonic Steklov problem
• Calderón problem for Yang-Mills connections
• On the relative heat invariants of the Dirichlet-to-Neumann operators associated with Schrödinger operators
• Heat invariants of the Steklov problem
• Asymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operator
• Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential
• Determining a magnetic Schrödinger operator from partial Cauchy data
• Schrödinger operators with singular potentials
• Beweis des Gaus'schen Integralsatzes
• Schrödinger operators in the twentieth century
• An Inverse Boundary Value Problem for Schrodinger Operators with Vector Potentials
• On the Analyticity of the Solutions of Analytic Non-Linear Elliptic Systems of Partial Differential Equations: Part I. Analyticity in the Interior
• Determining anisotropic real-analytic conductivities by boundary measurements
• Bose-Einstein condensates in the presence of a magnetic trap and optical lattice
• Can One Hear the Shape of a Drum? Revisited
• Determinant of the Neumann Operator on Smooth Jordan Curves
• Logarithmic terms in asymptotic expansions of heat operator traces
• Tauberian Theory
• Inverse problems: seeing the unseen
• On the asymptotic number of edge states for magnetic Schrödinger operators
• Can One Hear the Shape of a Drum?
• The Resolvent of an Elliptic Boundary Problem
• Generation of Analytic Semigroups by Strongly Elliptic Operators
• The Asymptotics of The Laplacian on a Manifold with Boundary
• Schrödinger operators with singular magnetic vector potentials
• Operator approach to linear problems of hydrodynamics. Vol. 1: Self-adjoint problems for an ideal fluid
• Global uniqueness in the inverse scattering problem for the Schrödinger operator with external Yang-Mills potentials
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