Abstract
Let {\(G = \mathbb{D} \times \mathbb{C}\)}, where {\(\mathbb{D}\)} is the open unit disk on the complex plane {\(\mathbb{C}\)}. In G, we consider analytic solutions u(t, z) ({\(t \in \mathbb{D}\)}, {\(z \in \mathbb{C}\)}) of the heat equation 2ut=uzz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have {\(\left\| {u, L^2 \left( {G,\mu } \right)} \right\| \leqslant C\left\| {f,L^2 \left( {\mathbb{C},e^{ - \left| z \right|^2 } } \right)} \right\|\)} Bibliography: 17 titles.
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155.
Translated by S. V. Kislyakov.
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Oleînik, V.L. Carleson measures and the heat equation. J Math Sci 101, 3133–3138 (2000). https://doi.org/10.1007/BF02673737
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DOI: https://doi.org/10.1007/BF02673737