Operator semistable probability measures on a Hilbert space

Injective Hilbert Space Embeddings of Probability Measures

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). The embedding function has been proven to be injective when the reproducing kernel is universal. In this...

On the Hilbert Space Embeddings and Metrics on Probability Measures

A Hilbert space embedding for probability measures has recently been proposed (Gretton et al., 2007; Smola et al., 2007), with applications including dimensionality reduction, homogeneity testing and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). Using this embedding, a pseudometric (let us define it as γk)...

Hilbert Space Embeddings and Metrics on Probability Measures

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). A pseudometric on the space of probability measures can be defined as the distance between distribution...

Operator Extensions on Hilbert Space

Spectral Theory of Operator Measures in Hilbert Space

In §2 the spaces L2(Σ,H) are described; this is a solution of a problem posed by M. G. Krĕın. In §3 unitary dilations are used to illustrate the techniques of operator measures. In particular, a simple proof of the Năımark dilation theorem is presented, together with an explicit construction of a resolution of the identity. In §4, the multiplicity function NΣ is introduced for an arbitrary (non...