论文标题
代表运算符的Berezin符号和光谱量度
Berezin symbols and spectral measures of representation operators
论文作者
论文摘要
让$ g $是一个谎言群体，带有Lie代数$ \ Mathfrak G $，让$π$是在复制的内核Hilbert Space上实现的$ G $的单一表示。我们使用berezin量化来研究与操作员$-IDπ（x）$相关的光谱测量，以$ x \ in {\ mathfrak g} $中的$ x \。作为应用程序，我们展示了有关谎言组表示收缩的结果如何产生频谱测量序列收敛的结果。我们给出了一些例子，包括$ su（1,1）$（1,1）$（2）$的宫缩。
Let $G$ be a Lie group with Lie algebra $\mathfrak g$ and let $π$ be a unitary representation of $G$ realized on a reproducing kernel Hilbert space. We use Berezin quantization to study spectral measures associated with operators $-idπ(X)$ for $X\in {\mathfrak g}$. As an application, we show how results about contractions of Lie group representations give rise to results on convergence of sequences of spectral measures. We give some examples including contractions of $SU(1,1)$ and $SU(2)$ to the Heisenberg group.
