Improvement of Pointwise Bounds for Eigenfunctions in the Quantum Completely Integrable System
MathematicsOn a compact n-dimensional Riemannian manifold without boundary (M,g), it is well-known that the L2-normalized Laplace eigenfunctions with semiclassical parameter h satisfy the universal L∞ growth bound of O(h1−n2)ash→0+.
Xianchao Wu
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Eigenfunction localization and nodal geometry on dumbbell domains [PDF]
, 2023 Saikat Maji, Soumyajit Saha
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Beyond the Hodge theorem: Curl and asymmetric pseudodifferential projections
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract We develop a new approach to the study of spectral asymmetry. Working with the operator curl:=∗d$\operatorname{curl}:={*}\mathrm{d}$ on a connected oriented closed Riemannian 3‐manifold, we construct, by means of microlocal analysis, the asymmetry operator — a scalar pseudodifferential operator of order −3$-3$.
Matteo Capoferri, Dmitri Vassiliev
wiley +1 more source
On one time-optimal control problem for a parabolic equation with involution in a bounded domain
AIMS MathematicsIn this paper, we study the problem of time-optimal control for the parabolic equation with involution in a multidimensional parallelepiped domain. A generalized solution to the initial boundary value problem is found, and the control problem is reduced ...
Farrukh Dekhkonov, Batirkhan Turmetov
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Value Distribution of the Eigenfunctions and Spectral Determinants of Quantum Star Graphs [PDF]
, 2003 Jonathan P. Keating +2 more
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Optimal Recovery of Rayleigh‐Wave Overtones by Multi‐Directional Acquisition
Geophysical Research LettersRayleigh waves are ubiquitously used for subsurface characterization through dispersion curve inversion, whose quality depends on the number of useable overtones.
A. Lellouch, E. Shimony, P. Sinitsyn
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On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori
, 2015 In this note, we discuss a question posed by T. Hoffmann-Ostenhof concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tori. We present two results.
Léna, Corentin
core
Eigenvalues and Eigenfunctions of One-Dimensional Fractal Laplacians [PDF]
, 2023 Wei Tang, Jia Guo
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Eigenfunction expansion for a regular fourth order eigenvalue problem with eigenvalue parameter in the boundry conditions [PDF]
, 1989 E. M. E. Zayed, S. F. M. Ibrahim
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