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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A fundamental solution of the parabolic equation on Hilbert space. II. The semigroup property

Author: M. Ann Piech
Journal: Trans. Amer. Math. Soc. 150 (1970), 257-286
MSC: Primary 47.50; Secondary 35.00
MathSciNet review: 0278116
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Abstract: The existence of a family of solution operators $ \{ {q_t}:t > 0\} $ corresponding to a fundamental solution of a second order infinite-dimensional differential equation of the form $ \partial u/\partial t = Lu$ was previously established by the author. In the present paper, it is established that these operators are nonnegative, and satisfy the condition $ {q_s}{q_t} = {q_{s + t}}$.

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Keywords: Hilbert space, abstract Wiener space, Wiener measure, parabolic equation, fundamental solution, semigroups of operators
Article copyright: © Copyright 1970 American Mathematical Society

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