Symmetric shift-invariant subspaces and harmonic maps

Boundary uniqueness of harmonic functions and spectral subspaces of operator groups

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on Banach spaces.

Harmonic maps and shift-invariant subspaces

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of operator-theoretic methods we derive a criterion for finiteness of the uniton number which has a large number of applications discussed in the paper.

A note on $k$-hyperreflexivity of Toeplitz-harmonic subspaces

The 2-hyperreflexivity of Toeplitz-harmonic type subspace generated by an isometry or a quasinormal operator is shown. The $k$-hyperreflexivity of the tensor product $\mathcal{S}\otimes \mathcal{V}$ of a $k$-hyperreflexive decomposable subspace $\mathcal{S}$ and an abelian von Neumann algebra $\mathcal{V}$ is established.

The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces

We consider the counter images $\maclJ (\rr d)$ and $\maclJ _0(\rr d)$ of entire functions with exponential and almost exponential bounds, respectively, under the Bargmann transform, and we characterize them by estimates of powers of the harmonic oscillator. We also consider the Pilipovi{ć} spaces $\bsycalS _s(\rr d)$ and $\bsySig _s(\rr d)$ when $0<s<1/2$ and deduce their images under the Bargmann transform.

Maps preserving common zeros between subspaces of vector-valued continuous functions

For metric spaces $X$ and $Y$, normed spaces $E$ and $F$, and certain subspaces $A(X,E)$ and $A(Y,F)$ of vector-valued continuous functions, we obtain a complete characterization of linear and bijective maps $T:A(X,E)\to A(Y,F)$ preserving common zeros, that is, maps satisfying the property \setcounter{equation}{15} \label{dub} Z(f)\cap Z(g)\neq \emptyset \Longleftrightarrow Z(Tf)\cap Z(Tg)\neq \emptyset for any $f,g\in A(X,E)$, where $Z(f)=\{x\in X:f(x)=0\}$. Moreover, we provide some examples of subspaces for which the automatic continuity of linear bijections having the property (\ref{dub})…

Lipschitz映射的自由线性化的不变子空间

Invariant subspaces for free linearizations of Lipschitz maps

该研究探讨Lipschitz自由空间上由Lipschitz自映射诱导算子的不变子空间问题，证明了特定条件下常规自由线性化$\boldsymbol{\textit{f}}$及算子$T_{f,e}$存在非平凡不变子空间，并给出线性动力学相关推论。