Questions tagged [semigroup-of-operators]

Question 1

I am studying a continuous-time Markov chain $(X_t)_{t \ge 0}$ on a countable state space $E$ with transition semigroup $(P_t)_{t \ge 0}$ acting on bounded functions $B(E)$. Strong (classical) ...

Question 2

Let $X$ be a Hilbert space with an orthonormal basis $f_j \in \mathcal D(C)$ where $C:\mathcal D(C)\subset X \to X$ is a linear (unbounded) operator (possibly generating a $C_0$ semigroup; you may ...

Question 3

Consider Schrödinger's equation $iu_t=Hu$ where the Hamiltonian $H=-\Delta+V$ has perturbation that is bounded on $L^2(\mathbb{R}^n)$. I cannot find any direct reference that the evolution operator $e^...

Question 4

For a problem of asymptotic stability, I found that the generator of my $C_0$-semigroup behaves differently if I consider the asymptotic operator, or the "rest" of the operator. I am trying ...

Question 5

I am studying the Lie-Trotter formula for operator exponentials. Let $H$ be a Hilbert space and $A$, $B$ be self-adjoint operators on $H$. The classical Lie-Trotter formula (see M. Reed, B. Simon. ...

Question 6

Let $e^{t \Delta}$ the heat semigroup on the torus, $f \in C^{a}(\mathbb{T}^2), g\in C^{-\varepsilon}(\mathbb{T^2})$, for $0<a<2$ and for each $\varepsilon>0$. I was able to find the ...

Question 7

I'm working on a expository research project that involves characterizing the infinitesimal generator of the fractional heat semigroup $\{P^t\}_{t\in\mathbb{R}_+}$(where $\widehat{P^tf}=e^{-t|\omega|^{...

Question 8

I was wondering if there is a way to define $e^{-At}$ for a linear unbounded operator $A$ where the spectrum $\sigma(A)$ of $A$ is contained in the shifted right half plane $\lbrace \lambda \in \...

Question 9

$H$ is a Hilbert space. $A,B,C$ are linear bounded operators on $H$. $P_0$ is a symmetric positive semidefinite linear bounded operator. Are the solutions of the following two operator valued Riccati ...

Question 10

A linear operator $A : \mbox{dom} A \subseteq X \to X$ is called sectorial of angle $\omega \in (0,\pi)$ if $S(\omega) := \lbrace \lambda \in \mathbb{C} : 0 < |\arg \lambda | < \omega \rbrace \...

Question 11

I’m reading nonlinear evolution equations by Song-Mu Zheng and I have some questions regarding the following statement THEOREM 2.4.1 ; COROLLARY 2.4.1 ; COROLLARY 2.4.2 ; COROLLARY 2.4.3 All are ...

Question 12

For $t\in \mathbb{R}$ let $m_t\colon \mathbb{R}\to \mathbb{R}, m_t(\xi)=e^{it|\xi|}$. The corresponding family of Fourier multiplier operators $(e^{it|D|})_{t\in \mathbb{R}}:=(m_t(D))_{t\in \mathbb{R}}...

Question 13

Today i need some explain to understand this let $X= C[(0,1)] $ and let $$Tf(x)=f^{\prime \prime}(x),$$ where $f\in C^{2}([0,1])\cap X$ and $f(0)=f(1)=0$ , be a closed linear operator. And let $g\in C^...

Question 14

I am having trouble understanding Lemma 20.10 from Souplet's book Superlinear Parabolic Problems, which provides a time decay estimate for the semigroup in a sectorial domain. I will first write the ...

Question 15

I'm reading some paper of PDE, in which they compute characteristic eqution by Laplace transform. For example,there is an equation and its boundary condition: $\partial_t u +\lambda\partial_x u=0$ $u(...

Stack Exchange Network

Questions tagged [semigroup-of-operators]

strong vs. weak infinitesimal generator

Let X Hilbert, C linear, $F:X\to D(C)$ s.t. $CF\in C^0$, $P_n$ projection. When $CP_n F :X \to X$ is uniformly continuous on compact, UNIFORMLY in n?

Invertibility of Schrödinger evolution

$C_0$ semi group split into the "essential" and "discrete" parts

Norm convergence in Lie-Trotter formula

Commutator bounds for the heat kernel on the torus

Are there any Banach Spaces that Bessel Potential Spaces are dense in?

Does a Sectorial operator of angle $\frac{\pi}{2}$ generate a semigroup?

The infinitesimal generator of operator valued Riccati equation

Sectorial operator with spectral bound $s(A) < 0$ implies exponential stability of induced $C_0$-Semigroup. [duplicate]

nonlinear evolution equations by Song-Mu Zheng Uniqueness of inhomogeneous PDE semigroup theory

Is the half-wave group in dimension one bounded on $L^\infty(\mathbb{R})$?

Estimation of $u(x)=e^{xB}B^{2}h(x)+e^{(1-x)B}B g(x)$ in holder space

How is the time decay of the heat semigroup in sectorial domains in $\mathbb{R}^N$ obtained?

Why Laplace transform can compute a characteristic eqution of a PDE

Hot Network Questions