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If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?

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#functional-analysis #partial-differential-equations #elliptic-equations #semigroup-of-operators #elliptic-operators
568
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Hille-Yoshida Theorem - help! Proving an operator generates a $C_0$ semigroup

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#functional-analysis #ordinary-differential-equations #semigroup-of-operators
207
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Proving an operator is surjective for Lumer-Phillips Theorem application.

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#functional-analysis #banach-spaces #semigroup-of-operators #contraction-operator
125
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Why does the Malliavin derivative of a Markovian semigroup being strong Feller imply the semigroup strong Feller?

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#stochastic-analysis #semigroup-of-operators #stochastic-pde #malliavin-calculus
195
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Semigroup of probability measures that transitions the laws of a process

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#probability-theory #stochastic-processes #stochastic-analysis #semigroup-of-operators
233
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Understanding a proof from Pazy's book on infinitesimal generators

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#functional-analysis #semigroup-of-operators
69
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$\{(T(t)f)(s) \; ;\; t \geq 0\}$ is a $C_0$ semigroup

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#functional-analysis #semigroup-of-operators
167
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Fundamental theorem of calculus for semigroups

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#stochastic-processes #markov-process #semigroup-of-operators
70
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Dynkin's theorem of extension of generators

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#stochastic-processes #markov-process #semigroup-of-operators
78
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Positivity preserving property of resolvents

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#stochastic-processes #markov-process #semigroup-of-operators
212
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Calculation/Verification of an integral kernel for $\operatorname{e}^{t\Delta}(1-\Delta)^{-\frac{1}{4}}$

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#laplace-transform #heat-equation #semigroup-of-operators #integral-operators
263
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Interpretation of the resolvent of Brownian motion

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#stochastic-processes #brownian-motion #markov-process #stopping-times #semigroup-of-operators
76
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Strengthening the strong Feller property

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#stochastic-processes #brownian-motion #markov-process #semigroup-of-operators
71
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Equality of two operators using (inverse) resolvent

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#functional-analysis #spectral-theory #semigroup-of-operators
68
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By definition of $e^{it\partial_x^2}, \partial_x^2 u \in L^2({\mathbb{T}}) $..

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#functional-analysis #semigroup-of-operators

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