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Results tagged with functional-calculus
Search options questions only
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user 54780
3
votes
0
answers
68
views
A strange convergence for a semigroup of operators
I am reading B. Simon's "Kato's inequality and the comparison of semigroups", and I am having troubles understanding a part of the proof of Theorem 1 therein, that goes as follows:
Let $A,B$ be semibo …
- 5,407
3
votes
1
answer
125
views
The imaginary exponential of a tangent field on a manifold
If $M$ is a compact Riemannian manifold and $X$ is a tangent field, I am seeking to define the object $\exp {\mathrm i t X}$ for $t \in \mathbb R$, and I do not know how to do it.
One option was …
- 5,407
0
votes
2
answers
132
views
The derivative of a $C_0$-semigroup with respect to a perturbation parameter
Let $H$ be a Hilbert space, and $A : H \to H$ be the (semi-bounded) generator of the $1$-parameter $C_0$-semigroup $[0, \infty) \ni t \mapsto \mathrm e ^{-t A}$. Let $B : H \to H$ be a bounded operato …
- 5,407