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Inversions of Hermite semigroup


Author: Du-Won Byun
Journal: Proc. Amer. Math. Soc. 118 (1993), 437-445
MSC: Primary 47D03; Secondary 33C45, 46E99, 46G99, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1993-1145414-6
MathSciNet review: 1145414
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \{ {e^{ - cH}}\vert c \geqslant 0\} $ be the Hermite semigroup on the real line $ \mathbb{R}$. Then a representation is constructed for inversions of the semigroup, and it gives a representation of $ {e^{ - cH}}$ for $ c < 0$. Moreover, some characterizations of the domain in which, for $ c < 0,\;{e^{ - cH}}$ is well defined are examined.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1145414-6
Keywords: Analytic extension, entire function, Hermite polynomial, Hermite semi-group, inverse of operator, positive matrix, reproducing kernel Hilbert space
Article copyright: © Copyright 1993 American Mathematical Society

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