Tagged Questions

A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). Of course, any monoid or group is also a semigroup.

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series representation for *un*bounded perturbations of semigroup generators

Let $A$ generate an analytic $C_0$-semigroup on a Banach space $X$ and $B$ be a relatively compact perturbation, i.e., $B$ is compact as an operator from $D(A)$ (with the graph norm) to $X$. Then $A+B$...
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Continuity of multiplicative character

Let $G$ be a discrete group and $\beta (G)$ denote the Stone-Cech compactification of $G$, a right topological semigroup. By a multiplicative character, I mean a mapping that preserves multiplication ...
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Heat semigroup ultracontractive?

Let $g(x,t)= \frac{1}{(4 \pi t)^{\frac{n}{2}}}e^{\frac{-|x|^2}{4t}}$ be the heat kernel on $\mathbb{R}^{n}.$ Is the standard definition now to say that this heat-semigroup $T(t)(f):=g *f(.,t)$ is ...
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Factorization of the Fokker-Planck semigroup

I have posted this question on stackexchange over four month ago, but didn't get an answer: "In the classical theory of Markov processes, the Fokker-Planck semigroup $\{T_t:t\ge 0\}$ can be factored ...
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Lower periodic subsets of groups and semigroups

Suppose that $A$ and $B$ are subsets of a group or semigroup. We call $A$ left upper [resp. lower] $B$-periodic if $BA\subseteq A$ [resp. $A\subseteq BA$]. If $A$ is both left upper and lower $B$-...
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Classification of rings between a PID and its field of fractions?

Let $D$ be a PID and let $\mathrm{Frac}(D)$ be its field of fractions. I want to classify the intermediate rings $D\subseteq R\subseteq \mathrm{Frac}(D)$. Theorem: Every such ring $R$ is a ...
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Given a differential equation on a Banach space $\mathcal{X}$ of the form $\frac{d u}{d t} = F(u)$, it is often the case that $F$ is equivariant under translations, i.e. that $T_\alpha F(u) = F(T_\... 0answers 78 views Embedding a cancellative monoid into another in such a way that$|X-x|=|X|$, where$X$is a fixed finite set and$x\in X$Preliminaries. Let$\mathbb A = (A, +)$be a possibly non-commutative semigroup. For$X, Y \subseteq A$we set $$X - Y := \{a \in A: a + y \in X\text{ for some }y \in Y\},$$ which is just the usual ... 0answers 66 views Is there a general theory for the structure of the (semi)group generated by morphisms of an affine space$F_p^3$? Consider an affine space$\mathbb{F}_p^3$, and assume we have a handful of morphisms$f_i : \mathbb{F}_p^3 \rightarrow \mathbb{F}_p^3$given by$$f_i(x, y, z) =(P_i(x, y, z), Q_i(x, y, z), R_i(x, y, z)... 0answers 51 views Decomposition results for locally commutative semigroups Every finite abelian group is the direct product of its cyclic groups of prime order, and every commutative monoid divides a product of its cyclic submonoids. Could these results generalized to ... 0answers 72 views Is there a strongly stable semigroup which is not uniformly bounded Let$X$be a Hilbert space and let$(T(t))_{t\geq 0}$a$C_0$-semigroup on$X$, we recall that: 1-$(T(t))_{t\geq 0}$is said to be uniformly bounded if there exists$M\geq 0$such that for all$t\...
If $G$ is a group which has a semigroup action on a regular rooted tree via prefix-preserving, continuous transformations (I give the tree the path metric), what kinds of algebraic restrictions can we ...