Abstract
The heat transform , for positive time , is the convolution on the complex plane with the heat kernel. In the field of analytic function spaces and related operator theory, coincides with the Berezin transform for the Fock space induced by the Gaussian measure . We study fixed-points of and the limit behavior of as . Fixed-points of are shown to be closely related to eigenfunctions of the Laplacian corresponding to certain special eigenvalues, while the limit behavior of as depends on certain continuity and oscillation properties of .
The paper is expository, although it contains a few new results. In particular, the main results about fixed-points of are known, but we present a completely new proof here.
Citation
Hasi Wulan. Jian Zhao. Kehe Zhu. "THE HEAT TRANSFORM ON THE COMPLEX PLANE." Rocky Mountain J. Math. 54 (1) 283 - 299, February 2024. https://doi.org/10.1216/rmj.2024.54.283
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