Uncertainty principle for Hermite functions and null-controllability with sensor sets of decaying density

DOI10.1007/S00041-022-09989-5OpenAlexW4317564964MaRDI QIDQ2686573

Alexander Dicke, Ivan Veselić, Albrecht Seelmann

Publication date: 28 February 2023

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.11703

zbMATH Keywords

Hermite functionsharmonic oscillatoruncertainty principlesnull-controllability

Mathematics Subject Classification ID

Controllability (93B05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Spectral theory and eigenvalue problems for partial differential equations (35Pxx) Qualitative properties of solutions to partial differential equations (35B99)

Related Items (4)

Controllability of the Schrödinger equation on unbounded domains without geometric control condition ⋮ Analyticity and observability for fractional order parabolic equations in the whole space ⋮ Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs ⋮ Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nodal sets of eigenfunctions on Riemannian manifolds
• Lectures on analysis on metric spaces
• Sharp geometric condition for null-controllability of the heat equation on \(\mathbb R^d\) and consistent estimates on the control cost
• Geometric conditions for the exact controllability of fractional free and harmonic Schrödinger equations
• Lower bounds for Dirichlet Laplacians and uncertainty principles
• Observable sets, potentials and Schrödinger equations
• Scale-free unique continuation estimates and Logvinenko-Sereda theorems on the torus
• Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains
• Observability of the heat equation, geometric constants in control theory, and a conjecture of Luc Miller
• Observable set, observability, interpolation inequality and spectral inequality for the heat equation in \(\mathbb{R}^n\)
• An abstract Logvinenko-Sereda type theorem for spectral subspaces
• Some results related to the Logvinenko-Sereda theorem
• On the null-controllability of diffusion equations
• On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
• Null-controllability of hypoelliptic quadratic differential equations
• Lecture notes on quantitative unique continuation for solutions of second order elliptic equations
• Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations
• Sharp estimates and homogenization of the control cost of the heat equation on large domains

This page was built for publication: Uncertainty principle for Hermite functions and null-controllability with sensor sets of decaying density