Abstract
We derive a new necessary and sufficient condition for solvability of a moment problem involving real exponentials, which arises in control theory for the heat equation; this allows one to identify some novel situations for which the moment problem is solvable. Moreover, we prove a theorem in the context of boundary control for the heat equation, which allows one to construct new reachable states from known reachable states; as a corollary this implies that all polynomial functions of the space variables are reachable. Finally, we show also that trigonometric polynomials (and certain related functions involving real exponentials) are also reachable.
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Communicated by A. V. Balakrishnan
This author wishes to thank the Mathematics Department at McGill University for its support and hospitality during the period in which this paper was completed.
This work was supported by the Natural Sciences and Engineering Research Council of Canada Grant A7271.
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Sachs, E., Georg Schmidt, E.J.P. On reachable states in boundary control for the heat equation, and an associated moment problem. Appl Math Optim 7, 225–232 (1981). https://doi.org/10.1007/BF01442117
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DOI: https://doi.org/10.1007/BF01442117