A fundamental solution of the parabolic equation on Hilbert space. II. The semigroup property
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- by M. Ann Piech PDF
- 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 ${q_s}{q_t} = {q_{s + t}}$.References
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Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 257-286
- MSC: Primary 47.50; Secondary 35.00
- DOI: https://doi.org/10.1090/S0002-9947-1970-0278116-8
- MathSciNet review: 0278116