33 papers
This paper extends interior non-concentration estimates for Laplace eigenfunctions to the boundary of compact smooth manifolds with boundary, demonstrating that these bounds, combined with a generalized sup-norm estimate, immediately yield the sharp bounds established by Grieser.
This paper reviews rigorous results on the semiclassical behavior of the scattering data for a non-self-adjoint Dirac operator with oscillatory potential, utilizing exact WKB and Olver's methods to advance the understanding of the focusing cubic NLS equation via inverse scattering theory.
This paper establishes the uniqueness of singular radial potentials in Schrödinger operators by proving that infinitely many Dirichlet spectra satisfying a Müntz-type condition determine the potential globally, while two spectra from specific distinct angular momenta ensure local uniqueness near the zero potential, thereby refining previous results and confirming a conjecture by Rundell and Sacks.
This paper constructs Patterson-Sullivan distributions on finite regular graphs via eigenfunction boundary values and establishes their connections to both Wigner distributions and invariant Ruelle distributions, thereby providing discrete analogues of key results from the study of quantum chaos on compact hyperbolic surfaces.
This paper employs subordinacy theory to characterize the spectral transitions from discrete to continuous spectra in several quantum Rabi models, proving the absence of singular spectrum and interior eigenvalues across all parameter ranges.
This paper classifies and analyzes exactly solvable one-dimensional complex Schrödinger operators related to the Gauss hypergeometric equation, organizing them into three geometric families (spherical, hyperbolic, and deSitterian) to compute their spectra and Green functions while establishing transmutation identities and linking them to symmetric manifolds.
This paper investigates heat equations with non-local Robin boundary conditions on bounded Lipschitz domains, demonstrating that while certain boundary operators can destroy the positivity-preserving property of the solution semigroup, the system still achieves ultracontractivity and exhibits eventual positivity under mild assumptions.
This paper presents various elementary approaches to elliptical range theorems for the Davis-Wielandt shell, numerical range, and conformal range, focusing on their quadratic representations.
This paper extends the study of resonance phenomena to doubly degenerate embedded eigenvalues by introducing a new concept utilizing the Morse Lemma to analyze rank-two self-adjoint perturbations of the Laplacian, thereby deriving asymptotic results for spectral density and characterizing key resonance properties such as sojourn time, scattering cross-section, and time delay.
This paper investigates the point spectrum of periodic quantum trees with delta-type vertex conditions, establishing analogs to discrete results while demonstrating that, unlike the discrete case, regular quantum periodic trees can possess eigenvalues, though these can be eliminated by arbitrarily small adjustments to edge lengths.
This paper establishes a Barta-type formulation for the -Laplacian on Riemannian manifolds to derive sharp lower bounds for the -fundamental tone without boundary regularity assumptions, leading to nonlinear extensions of classical spectral comparison theorems and geometric characterizations for minimal immersions.
This paper establishes sharp uniform bounds on the eigenvalues of time-frequency localization operators and coherent state transform localizations near their spectral phase transition, revealing a qualitative difference in their decay rates where the former exhibits a logarithmic dependence while the latter decays quadratically.
This paper summarizes existing results and open questions regarding isometric embeddings between Schatten classes, provides an overview of relevant methods, and establishes a new non-embeddability result using a novel approach.
This paper establishes conditions for the distance integrality of specific graph families constructed via joins with cycles and for the distance Laplacian integrality of a particular class of dumbbell graphs.
This paper establishes both Anderson localization and Hölder continuity of the integrated density of states for quasi-periodic Schrödinger operators on with non-constant analytic potentials and fixed Diophantine frequencies in the perturbative regime, utilizing a novel multi-scale analysis approach to control Green's functions.
This paper investigates matrices and operators satisfying the Kreiss condition with constants arbitrarily close to one, establishing refined lower bounds for power growth and demonstrating that specific variants of the condition guarantee similarity to a contraction when the spectrum touches the unit circle at a single point, utilizing a positivity argument involving the double-layer potential operator.
This paper disproves the Perälä–Virtanen conjecture by constructing explicit radial symbols on Bergman and Fock spaces where a positive limit inferior of the Berezin transform fails to guarantee essential positivity, demonstrating that the Berezin liminf criterion is insufficient for radial Toeplitz operators in all complex dimensions.
This paper establishes a unified framework for estimating the spectral deviation of concentration operators on reproducing kernel Hilbert spaces, demonstrating that discretized approximations like Gabor multipliers preserve the theoretical localization properties of their continuous counterparts with bounds uniform in the discretization step.
This paper establishes a uniform upper bound for the eigenvalues of the Hodge Laplacian on closed Riemannian manifolds with lower bounds on Ricci curvature and injectivity radius, as well as an upper bound on diameter, thereby extending Cheng-type eigenvalue comparison theorems to differential forms without requiring sectional curvature bounds.
This paper proves that for the fractional Laplacian with nonlocal Neumann boundary conditions in an -dimensional ball, the eigenspace corresponding to the first nontrivial eigenvalue is generated by antisymmetric eigenfunctions with exactly two nodal domains when the fractional order is sufficiently close to 1.