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Transactions of the American Mathematical Society
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0278116-8
PII: S 0002-9947(1970)0278116-8
Keywords: Hilbert space, abstract Wiener space, Wiener measure, parabolic equation, fundamental solution, semigroups of operators
Article copyright: © Copyright 1970 American Mathematical Society