第三章我们从庞加莱群着手构造合适的希尔伯特空间的多种幺正表象。
In the third chapter we start with the Poincare group and construct various unitary representations in suitable Hilbert spaces.
在有限维希尔伯特空间中构造了非简谐振子的广义相干态，并研究了其量子统计特性。
Generalized coherent states of a non harmonic oscillator in a finite dimensional Hilbert space are constructed and some quantum statistical properties are studied.
讨论描述希尔伯特空间最终范数连续半群特征的一个算子方程的解，给出这个解的一个显式表达式。
A new perturbation result on the Hilbert space for the eventually norm-continuous semigroups is obtained, which makes the perturbation of the semigroups more abundant.
我们将详细的讨论核心课程中十分重要的特质，其引导出再生核希尔伯特空间理论(RKHS)中一个非常关键的概念。
We discuss at length the properties of a very important class of kernels which lead to the key notion of Reproducing kernel Hilbert Space (RKHS).
在量子语境中的解释“不”意为把“song”作为在称为语义环境的多维希尔伯特空间中的标志，所有有相同意思的单词都集中在这个标志附近。
Interpreting "not" in the quantum sense means taking "songs" as an arrow in a multidimensional Hilbert space called semantic space, where words with the same meaning are grouped together.
在量子语境中的解释“不”意为把“song”作为在称为语义环境的多维希尔伯特空间中的标志，所有有相同意思的单词都集中在这个标志附近。
Interpreting "not" in the quantum sense means taking "songs" as an arrow in a multidimensional Hilbert space called semantic space, where words with the same meaning are grouped together.
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