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

Piech, M. Ann

doi:10.1090/S0002-9947-1970-0278116-8

A fundamental solution of the parabolic equation on Hilbert space. II. The semigroup property
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Trans. Amer. Math. Soc. 150 (1970), 257-286 Request permission

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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