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Growth of Taylor coefficients over complex homogeneous spaces
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Driver Bruce K.
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Gross Leonard
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Saloff-Coste Laurent
… Fixing a positive time, we may form the Hilbert space of holomorphic functions on the group which are square integrable with respect to this heat kernel measure. … In previous work we have shown that, for each positive time, the Taylor map, which sends a holomorphic function to its set of Taylor coefficients at the identity element, is a unitary map from the previous Hilbert space of square integrable holomorphic functions onto a Hilbert space contained in the dual of the universal enveloping algebra. …
Tohoku mathematical journal. Second series 62(3), 427-474, 2010-09