Lieb-Thirring inequalities and other functional inequalities for orthonormal systems

DOI10.4171/icm2022/105arXiv2109.13660OpenAlexW3202843103MaRDI QIDQ6200703

Rupert L. Frank

Publication date: 24 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.13660

zbMATH Keywords

Sobolev inequalityStrichartz inequalityorthonormal systemsLieb-Thirring inequalityFourier restriction inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Applications of operator theory in the physical sciences (47N50) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Harmonic analysis and PDEs (42B37) Inequalities in real analysis (26Dxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximizers for the Stein-Tomas inequality
• Hardy and Lieb-Thirring inequalities for anyons
• Strichartz inequality for orthonormal functions
• The Hartree equation for infinitely many particles. II: Dispersion and scattering in 2D
• The Stein-Tomas inequality in trace ideals
• Endpoint resolvent estimates for compact Riemannian manifolds
• Balanced distribution-energy inequalities and related entropy bounds
• An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators
• Spectral density and Sobolev inequalities for pure and mixed states
• Maximal estimates for the Schrödinger equation with orthonormal initial data
• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• An \(L^ p\) bound for the Riesz and Bessel potentials of orthonormal functions
• A new proof of the Cwikel-Lieb-Rosenbljum bound
• Relativistic stability of matter. I
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• On Wigner measures
• The Rozenblum-Lieb-Cwikel inequality for Markov generators
• Sharp Lieb-Thirring inequalities in high dimensions.
• Littlewood-Paley decomposition of operator densities and application to a new proof of the Lieb-Thirring inequality
• Eigenvalue bounds for Schrödinger operators with complex potentials II
• Lieb-Thirring inequality with semiclassical constant and gradient error term
• Sharp resolvent estimates outside of the uniform boundedness range
• Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces
• The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities
• The Lieb-Thirring inequality revisited
• The periodic Lieb-Thirring inequality
• The Hartree equation for infinitely many particles. I: Well-posedness theory
• On the Strichartz estimates for orthonormal systems of initial data with regularity
• Cwikel's theorem and the CLR inequality
• Maximizers for the Strichartz inequality
• Global maximizers for the sphere adjoint Fourier restriction inequality
• On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds
• On the number of eigenvalues of Schrödinger operators with complex potentials
• On the Strichartz Estimates for the Kinetic Transport Equation
• Equivalence of Sobolev inequalities and Lieb-Thirring inequalities
• On L^p resolvent estimates for Laplace–Beltrami operators on compact manifolds
• Endpoint Strichartz estimates
• Eigenvalue bounds for Schrödinger operators with complex potentials. III
• Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
• Spectral Problems Related to the Critical Exponent in the Sobolev Embedding Theorem
• BOUND STATES FOR SCHRÖDINGER HAMILTONIANS: PHASE SPACE METHODS AND APPLICATIONS
• Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities
• Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
• Eigenvalue bounds for Schrödinger operators with complex potentials
• Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains
• The Lieb–Thirring inequalities: Recent results and open problems
• A restriction theorem for the Fourier transform

This page was built for publication: Lieb-Thirring inequalities and other functional inequalities for orthonormal systems