Question

When are spectral values a pole of the resolvent?

score 268 · Answer 1 · 2020-04-30 14:24:24

268

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When are spectral values a pole of the resolvent?

Published on 30 Apr 2020 - 14:24

score 60 · Answer 2 · 2020-05-06 15:11:50

60

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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 06 May 2020 - 15:11

score 119 · Answer 3 · 2026-03-25 17:43:33

119

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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

score 57 · Answer 4 · 2026-03-25 23:42:45

57

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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

score 201 · Answer 5 · 2026-03-25 12:16:26

201

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On the resolvent set of an unbounded operator

Published on 25 Mar 2026 - 12:16

score 72 · Answer 6 · 2026-02-23 04:58:23

72

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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 23 Feb 2026 - 4:58

score 56 · Answer 7 · 2020-06-12 14:45:16

56

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

Published on 12 Jun 2020 - 14:45

score 111 · Answer 8 · 2020-06-19 10:24:27

111

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Norm of the resolvent and inequalities

Published on 19 Jun 2020 - 10:24

score 234 · Answer 9 · 2020-06-19 13:38:58

234

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

Published on 19 Jun 2020 - 13:38

score 129 · Answer 10 · 2020-07-03 04:15:03

129

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In this situation we can shift path of integration?

Published on 03 Jul 2020 - 4:15

score 87 · Answer 11 · 2020-07-04 18:13:11

87

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Using Cauchy's theorem

Published on 04 Jul 2020 - 18:13

score 50 · Answer 12 · 2020-07-06 19:35:25

50

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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 06 Jul 2020 - 19:35

score 84 · Answer 13 · 2020-07-09 13:27:23

84

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Can I show this using a contraction semigroup property?

Published on 09 Jul 2020 - 13:27

score 74 · Answer 14 · 2020-07-14 14:59:25

74

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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 14 Jul 2020 - 14:59

score 186 · Answer 15 · 2026-03-24 16:48:21

186

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List of diffusion processes with known transition probabilities

Published on 24 Mar 2026 - 16:48

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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