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Questions tagged [semigroup-of-operators]

For questions related to theory of semigroups of linear operators and its applications to partial differential equations, stochastic processes such as Markov processes and other branches of mathematics.

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A question about Schrödinger semigroups

The question is about Theorem 14.1 in Teschl's Partial Differential Equations which goes like that $\textbf{Theorem 14.1.}$ The family $T_S(t)$ is a $C_0$-group in $H^{r}(\mathbb{R}^{n})$ whose ...
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Perturbation of uniformly continuous semigroup

I think I can prove the following claim about perturbing semigroups, but this must be known somehow, and I am just reinventing the wheel. Do you have any suggestions for references that treat this, ...
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What is the importance of Banach space in the theory of semigroups of linear operators?

Pazy's book defines semigroups as follows. Let $X$ be a Banach space. A one parameter family $T(t)$, $0< t < \infty$, of bounded linear operators from $X$ into $X$ is a semigroup of bounded ...
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Heat semigroup in Heisenberg groups properties

I'm trying to find the construction of the heat semigroup in Heisenberg groups, but I haven't found anything. In particular, I'm trying to find out if the semigroup in the Heisenberg group has the ...
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Semigroup of heat equation: $\|P^\kappa_t \|_{L^p \to L^{p'}} \le c t^{-\frac{d(p'-p)}{2pp'}}$

For any $\kappa>0$, we consider the Gaussian heat kernel $$p^\kappa_t (x) := (\kappa \pi t)^{-\frac{d}{2}} e^{-\frac{|x|^2}{\kappa t}}, \quad t>0, x \in {\mathbb R}^d.$$ Let \$L^0 := L^0 (\...
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