Theory of reproducing kernels for Hilbert spaces of vector valued functions

By George R. Pedrick. 1957

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Learning Theory for Distribution Regression (2014, methodology): “The kernel (say KG) is defined on M + 1 (X), and the regressor is then modelled by an element in the RKHS G = G(KG) of functions mapping from M + 1 (X) to Y .”
VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM (2006, background): “Our results hold for RKH spaces of functions f : X → K where X is a measurable set and K is a Hilbert space, following the general setting of vector valued RKH spaces outlined in [1, 2, 3].”
Vector valued reproducing kernel Hilbert spaces and universality (2008, background): “The theory of vector valued RKHS has been completely worked out in the seminal paper [27], devoted to the characterization of the Hilbert spaces that are continuously embedded into a locally convex topological vector space, see [23].”
Input Output Kernel Regression (2016, methodology): “When functions are vector-valued, the adequate RKHS theory makes use of operator-valued kernels (Pedrick, 1957; Senkene and Tempel’man, 1973; Micchelli and Pontil, 2005).”