2024
DOI: 10.1007/s00013-024-02051-4
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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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