103 problems

Let $X$ and $U$ be Hilbert spaces, and let $B$ be an input operator. The resolvent condition is the estimate denoted by … should be equivalent when $X$ and $U$ are Hilbert spaces.…

Let $(T(t))_{t\geq 0}$ be a bounded semigroup on a Hilbert space $X$ with infinitesimal generator $-A$ such that $\sigma(A)\cap i\mathbb{R}=\emptyset$. Define … and let…

Freeness conjecture. Every maximal subgroup of $\operatorname{IG}(\mathcal{E})$ is a free group.

Let $K$ be a number field and let $S$ be a finite set of places of $K$ containing all archimedean ones. Let $f_1,\ldots,f_s:\mathbb{P}^1\to\mathbb{P}^1$ be rational maps of degree…

Let $(\phi_t)$ be a parabolic semigroup of zero hyperbolic step in the unit disk, with Denjoy–Wolff point $\tau$. The slope is the cluster set of $\arg(1-\overline{\tau}\phi_t(z))$…

Hinkkanen–Martin's modified conjecture. For all $f,g\in G$, one has

Let $\mathfrak{h}$ be the Cartan subalgebra and let $\Lambda$ denote the set of parameters for which the corresponding quantization exists, viewed as a semigroup under the semigrou…

Rigidity conjecture. The conjectured rigidity assertion is not recoverable from the supplied statement span.

Optimality conjecture. The exponent $\gamma'=\frac{\gamma}{1-\gamma}$ is optimal.

Let ${\cal W}$ be the wild integer semigroup, and let $n$ be an element of ${\cal W}$. Weak $3x+1$ conjecture. If $n$ belongs to ${\cal W}$, then $n/k$ also belongs to ${\cal W}$ f…

Let $(X,r)$ be a square-free solution of the set-theoretic Yang–Baxter equation, and let $S(X,r)$ be its associated semigroup. For $x,y,x',y'\in X$, write $r(xy)=y'x'$. Conjectures…

Let $(X,r)$ be a square-free, nondegenerate, involutive solution of the set-theoretic Yang–Baxter equation, with associated semigroup $S(X,r)$. Skew-polynomial ordering conjecture.…

The paper considers one-parameter semigroups whose generators are elliptic operators of order greater than two. In particular, examples on $L^1(\mathbb{R}^n)$ can have uniformly bo…

Let $\sigma\subset\mathbb{Q}^n$ be a not necessarily convex cone, let $L^*\subset\mathbb{Q}^n$ be the dual lattice, and let $V=\{v_1,\ldots,v_m\}\subset L^*$. Let $S_\sigma$ denote…

Let $\mathfrak{ns}$ be the Neveu–Schwarz algebra, let $\rho_{h,c}$ be a highest weight representation of $\mathfrak{ns}$, and let $\EuScript H_\infty[\EuScript A]$ be the correspon…

Let $(e^{tL})_{t\geq 0}$ be a $C_0$-semigroup in a Banach space $\mathcal{F}$ with generator $(L,D(L))$. Let $G$ be a Chernoff function for $L$ satisfying condition (N) or (N'). Fi…

For $2\leq p<8$, let $t'_p$ denote the optimal time and let $\beta$ be the parameter of the quantum Ornstein–Uhlenbeck semigroup. There are positive constants…

Let $G$ be a finite abelian group, and regard its underlying set with the monoid structure obtained by adjoining an identity in the semigroup construction denoted $G^e$. The number…

Let $S$ be a finite commutative semigroup with zero, and let $G(S)$ be its zero-divisor graph. The graph $G(S)$ is complemented if every vertex $a$ has an orthogonal vertex $b$, me…

Let $S$ be a finite commutative semigroup with zero, and let $G(S)$ be its zero-divisor graph. A graph is complemented if every vertex is orthogonal to some vertex, where adjacent…

Let $\mathcal{S}$ be a unital commutative semigroup, possibly with the cancellation property, and let $\pi$ be a frame representation of $\mathcal{S}$. Let $\mathcal{A}$ be the…

Let $P$ be a non-injective polynomial and let $f$ be a transcendental entire map. The semigroup $\langle P,f\rangle$ is the semigroup generated by $P$ and $f$. Freeness conjecture.…

Let $G$ be a simply connected complex algebraic group with Lie algebra $mathop{mathrm{Lie}}G=mathfrak{g}$, let $U$ be a maximal unipotent subgroup of $G$, and set … For a subalgeb…

Let $G_r$ be the nonlinear resolvent associated with $r>0$, and let $q$ and $\gamma_r$ be the parameters defined in the paper. The semigroup generated by $G_r$ is considered with r…

Let $S=\{2^m3^n:m,n\in\mathbb{N}\}$. A measure-preserving system is totally ergodic if every positive power of its transformation is ergodic, and a set is good for measurable recur…