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Orthogonality from disjoint support in reproducing kernel Hilbert spaces. (English) Zbl 1159.46014
Summary: We investigate reproducing kernel Hilbert spaces (RKHS) where two functions are orthogonal whenever they have disjoint support. Necessary and sufficient conditions in terms of feature maps for the reproducing kernel are established. We also present concrete examples of finite dimensional RKHS and RKHS with a translation invariant reproducing kernel. In particular, it is shown that a Sobolev space has the orthogonality from disjoint support property if and only if it is of integer index.

MSC:
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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