List questions from semigroup-of-operators

Published on 26 Mar 2026 - 1:34

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What can we infer from a growth bound What can we infer from the condition $\limsup_{n\to\infty}\frac{\ln\left\|A_n\right\|}n\le0$?

Published on 26 Mar 2026 - 1:29

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Question on Semigroup theory for evolution equations: Strong continuity of analytic semigroup $e^{-tA}$

Published on 25 Mar 2026 - 17:43

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For $T(t)$ strongly continuous, check that $T(t)x - x = tAx + \int_0^t (t-s) T(s)A^2 x ds$.

Published on 25 Mar 2026 - 23:42

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On the resolvent set of an unbounded operator

Published on 25 Mar 2026 - 12:16

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If $X:\Omega\times[0,\infty)\times E\to E$ is a stochatic flow, is $\kappa_t(x,B):=\operatorname P\left[X^x_t\in B\right]$ a semigroup?

Published on 09 Apr 2026 - 12:03

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Extend a bound for a Markov semigroup using Jensen's inequality

Published on 26 Mar 2026 - 1:26

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Norm of the resolvent and inequalities

Published on 26 Mar 2026 - 1:34

235

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Strong continuity of the heat semigroup in $L^2(\mathbb{R}^n)$.

Published on 26 Mar 2026 - 1:34

130

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In this situation we can shift path of integration?

Published on 26 Mar 2026 - 1:29

88

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Using Cauchy's theorem

Published on 26 Mar 2026 - 3:09

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$\lim_{\epsilon \to 0} \frac{1}{\epsilon} \int_0^\epsilon e^{-\alpha s}P_s uds = u$ for Feller semigroup

Published on 26 Mar 2026 - 1:29

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Can I show this using a contraction semigroup property?

Published on 26 Mar 2026 - 1:26

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If $\frac{{\rm d}X^{s,\:x}}{{\rm d}t}(t)=v(t,X^{s,\:x}(t))$ and $X^{s,\:x}_s=x$, can we show that $X^{s,\:X^{r,\:x}(s)}(t)=X^{r,\:x}(s+t)$?

Published on 26 Mar 2026 - 1:29

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List of diffusion processes with known transition probabilities

Published on 25 Apr 2026 - 7:30

List Question

When are spectral values a pole of the resolvent?

What can we infer from a growth bound What can we infer from the condition $\limsup_{n\to\infty}\frac{\ln\left\|A_n\right\|}n\le0$?

Question on Semigroup theory for evolution equations: Strong continuity of analytic semigroup $e^{-tA}$

For $T(t)$ strongly continuous, check that $T(t)x - x = tAx + \int_0^t (t-s) T(s)A^2 x ds$.

On the resolvent set of an unbounded operator

If $X:\Omega\times[0,\infty)\times E\to E$ is a stochatic flow, is $\kappa_t(x,B):=\operatorname P\left[X^x_t\in B\right]$ a semigroup?

Extend a bound for a Markov semigroup using Jensen's inequality

Norm of the resolvent and inequalities

Strong continuity of the heat semigroup in $L^2(\mathbb{R}^n)$.

In this situation we can shift path of integration?

Using Cauchy's theorem

$\lim_{\epsilon \to 0} \frac{1}{\epsilon} \int_0^\epsilon e^{-\alpha s}P_s uds = u$ for Feller semigroup

Can I show this using a contraction semigroup property?

If $\frac{{\rm d}X^{s,\:x}}{{\rm d}t}(t)=v(t,X^{s,\:x}(t))$ and $X^{s,\:x}_s=x$, can we show that $X^{s,\:X^{r,\:x}(s)}(t)=X^{r,\:x}(s+t)$?

List of diffusion processes with known transition probabilities

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