Summary
Relations between such transcendental differential operators asexp tD 2x andexp xD 1/2t are obtained. A new characterization of temperature functions represented by the classicalPoisson integral is obtained, as well as one for positive temperature functions.
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Widder, D.V. Integral transforms related to heat conduction. Annali di Matematica 42, 279–305 (1956). https://doi.org/10.1007/BF02411881
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DOI: https://doi.org/10.1007/BF02411881