Spherical Logvinenko–Sereda–Kovrijkine type inequality and null-controllability of the heat equation on the sphere
Alexander Dicke,
Ivan Veselić
Abstract:It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko–Sereda–Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spectral inequality for the Laplace–Beltrami operator, which, in turn, yields observability and null-controllability with explicit estimates on the control costs for the spherical heat equation that are sharp in the large and in the small time regime.
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