无限维向量丛的再生核与正性
Reproducing kernels and positivity of vector bundles in infinite dimensions
摘要：
我们研究了无限维Hermitian向量丛上再生核的存在性与相应丛的正性之间的相互作用。正性是指与再生核相关的某些共变导数在所考虑的向量丛上的曲率形式。曲率形式的值是希尔伯特空间算子，因此它的正性可以从算子理论的通常意义上理解。
英文摘要：
We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain covariant derivatives associated to reproducing kernels on the vector bundles under consideration. The values of the curvature form are Hilbert space operators, and its positivity is thus understood in the usual sense from operator theory.
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