再生核希尔伯特空间入门
A Primer on Reproducing Kernel Hilbert Spaces
摘要：
再生核希尔伯特空间的阐述，而不假定事先熟悉希尔伯特空间。与现有的教学材料相比，更关心的是激励再生核希尔伯特空间的定义，并解释何时以及为什么这些空间是有效的。新的观点是再生核希尔伯特空间理论研究的是外几何，它把每一种几何构形与一个规范的超定坐标系联系起来。这个坐标系随着几何构型的变化而不断变化，使得它非常适合于研究那些解也随着几何构型的变化而不断变化的问题。这本入门书也可以作为无限维线性代数的入门，因为再生核希尔伯特空间比更一般的希尔伯特空间有更多与欧几里得空间相同的性质。
英文摘要：
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious. The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geometry, associating with each geometric configuration a canonical overdetermined coordinate system. This coordinate system varies continuously with changing geometric configurations, making it well-suited for studying problems whose solutions also vary continuously with changing geometry. This primer can also serve as an introduction to infinite-dimensional linear algebra because reproducing kernel Hilbert spaces have more properties in common with Euclidean spaces than do more general Hilbert spaces.
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