From the reachable space of the heat equation to Hilbert spaces of holomorphic functions

DOI10.4171/JEMS/989zbMath1454.93022OpenAlexW2768255669MaRDI QIDQ2216739

Karim Kellay, Andreas Hartmann, Marius Tucsnak

Publication date: 17 December 2020

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/989

zbMATH Keywords

Riesz basisheat equationBergman spacesHardy-Smirnov spacesGaussiansreachable space

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Heat equation (35K05) Control/observation systems in abstract spaces (93C25) Attainable sets, reachability (93B03) Hardy spaces (30H10) Heat kernel (35K08) Bergman spaces and Fock spaces (30H20)

Related Items

Reachable Space of the Hermite Heat Equation with Boundary Control ⋮ Reachable states for the distributed control of the heat equation ⋮ Analytic properties of heat equation solutions and reachable sets ⋮ Reachability results for perturbed heat equations ⋮ Sharp reachability results for the heat equation in one space dimension ⋮ Reachable states for infinite-dimensional linear systems: old and new ⋮ The weighted Bergman space on a sector and a degenerate parabolic equation ⋮ Reachable states and holomorphic function spaces for the 1-D heat equation ⋮ On the Reachable Set for the One-Dimensional Heat Equation ⋮ Separation of singularities for the Bergman space and application to control theory ⋮ The reachable space of the heat equation for a finite rod as a reproducing kernel Hilbert space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Flatness for a strongly degenerate 1-D parabolic equation
• Time-invariance of the reachable set for linear control problems
• Null controllability of the heat equation using flatness
• On the cost of observability in small times for the one-dimensional heat equation
• New blow-up rates for fast controls of Schrödinger and heat equations
• Exact controllability theorems for linear parabolic equations in one space dimension
• Null Controllability of One-dimensional Parabolic Equations by the Flatness Approach
• The bergman space on a sector and the heat equation
• Even More States Reachable by Boundary Control for the Heat Equation
• Reachable states in boundary control of the heat equation are independent of time
• On the Reachable Set for the One-Dimensional Heat Equation
• On the Reachable States for the Boundary Control of the Heat Equation
• Minimal controllability time for the heat equation under unilateral state or control constraints