Question

A good reference to begin Operator Semigroups

score 698 · Answer 1 · 2026-03-24 11:54:46

698

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A good reference to begin Operator Semigroups

Published on 24 Mar 2026 - 11:54

score 121 · Answer 2 · 2026-03-25 07:42:26

121

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If $S$ is a strongly continuous semigroup on a Hilbert space $H$ and $u\in C^1((0,T),H)$, show that $\lim_{h\to0+}S(h)\frac{u(s)-u(s-h)}h=u'(s)$

Published on 25 Mar 2026 - 7:42

score 406 · Answer 3 · 2026-03-25 10:22:04

406

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If $T$ is a strongly continuous semigroup, then $t\mapsto T(t)x$ is differentiable, for all $x$

Published on 25 Mar 2026 - 10:22

score 91 · Answer 4 · 2026-03-24 23:05:26

91

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How is the fundamental theorem of calculus used in a proof about the mild representation formula for the solution to an abstract ODE that I'm reading?

Published on 24 Mar 2026 - 23:05

score 78 · Answer 5 · 2026-03-25 15:43:48

78

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why $\int_\Omega S(t) div(w) = \int_\Omega div(w)$ ? where $S(t)$ is a heat semigroup with neumann condition

Published on 25 Mar 2026 - 15:43

score 518 · Answer 6 · 2026-03-24 17:46:57

518

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Core of linear operator

Published on 24 Mar 2026 - 17:46

score 28 · Answer 7 · 2026-03-25 04:33:37

28

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Adjoints of similar operators

Published on 25 Mar 2026 - 4:33

score 1k · Answer 8 · 2026-03-25 11:38:13

1k

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Semi-group theory and Poisson equation on the upper half plane

Published on 25 Mar 2026 - 11:38

score 213 · Answer 9 · 2026-03-25 08:59:46

213

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If a closed linear operator is one to one on a dense set, then is it one to one on the whole set?

Published on 25 Mar 2026 - 8:59

score 53 · Answer 10 · 2026-03-24 20:37:08

53

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Proof of a Proposition that generators uniquely determine strongly continuous contraction semigroups

Published on 24 Mar 2026 - 20:37

score 64 · Answer 11 · 2026-03-25 07:42:05

64

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If $A$ is a closable linear operator with domain $D(A)$ then if $f_n \in D(A)$ is $\lim_n f_n$ in $D(\bar{A})$?

Published on 25 Mar 2026 - 7:42

score 152 · Answer 12 · 2026-03-25 09:59:32

152

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Help understand the proof of the Multivalued opertor version of the Hille-Yosida Theorem in Ethier-Kurtz

Published on 25 Mar 2026 - 9:59

score 31 · Answer 13 · 2026-03-25 08:34:25

31

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Ethier-Kurtz : Showing that the extended limit of the sequence $A_n$ is closed.

Published on 25 Mar 2026 - 8:34

score 529 · Answer 14 · 2026-03-25 00:04:15

529

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Heat equation: Regularity of solution for initial conditions not in the domain but smooth

Published on 25 Mar 2026 - 0:04

score 144 · Answer 15 · 2026-03-25 03:23:14

144

Views

Is the notion of limit in Trotter Kurtz approximation theorem well defined? A Question concerning the paper of Kurtz (1969))

Published on 25 Mar 2026 - 3:23

List Question

A good reference to begin Operator Semigroups

If $S$ is a strongly continuous semigroup on a Hilbert space $H$ and $u\in C^1((0,T),H)$, show that $\lim_{h\to0+}S(h)\frac{u(s)-u(s-h)}h=u'(s)$

If $T$ is a strongly continuous semigroup, then $t\mapsto T(t)x$ is differentiable, for all $x$

How is the fundamental theorem of calculus used in a proof about the mild representation formula for the solution to an abstract ODE that I'm reading?

why $\int_\Omega S(t) div(w) = \int_\Omega div(w)$ ? where $S(t)$ is a heat semigroup with neumann condition

Core of linear operator

Adjoints of similar operators

Semi-group theory and Poisson equation on the upper half plane

If a closed linear operator is one to one on a dense set, then is it one to one on the whole set?

Proof of a Proposition that generators uniquely determine strongly continuous contraction semigroups

If $A$ is a closable linear operator with domain $D(A)$ then if $f_n \in D(A)$ is $\lim_n f_n$ in $D(\bar{A})$?

Help understand the proof of the Multivalued opertor version of the Hille-Yosida Theorem in Ethier-Kurtz

Ethier-Kurtz : Showing that the extended limit of the sequence $A_n$ is closed.

Heat equation: Regularity of solution for initial conditions not in the domain but smooth

Is the notion of limit in Trotter Kurtz approximation theorem well defined? A Question concerning the paper of Kurtz (1969))

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