Let $A$ be a symmetric, semi bounded (say WLOG positive) operator. Let $(A_1,D(A_1)), (A_2,D(A_2))$ be two positive, self adjoint extensions of $A$. Then the $-A_i$ generate two $C_0$ semigroups $S_i$. I was wondering if anything is known on the relationship between the two semigroups. Ideally one would want them to be the same so that one could give an unambiguous meaning to solutions of the equation $\partial_tu=-Au$, but I don’t see any reason why this should be true. Thanks in advance!
2026-04-02 05:27:07.1775107627
Reference request: semigroups generated by two different self-adjoint extensions
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