It is known that in the field of learning theory based on reproducing kernel Hilbert spaces the upper bounds estimate for a K-functional is needed. In the present paper, the upper bounds for the K-functional on the unit sphere are estimated with spherical harmonics approximation. The results show that convergence rate of the K-functional depends upon the smoothness of both the approximated func...

For pairs of density operators on nite dimensional Hilbert spaces we deene partial delities, prove their concavity and other properties. Partial delities characterize equivalence classes which are partially ordered in a natural way.

Some inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.

where A is the infinitesimal generator of the C0-semigroup T (t) on the state space X, B is a bounded linear operator from input space U to X, C is a bounded linear operator from X to the output space Y , and D is a bounded operator from U to Y . The spaces X, U and Y are assumed to be Banach spaces. More detail on the system (1) can be found in Curtain and Zwart [1]. For the system (1) we intr...

A circuit realization is presented for generalized one-multiplier lattice discrete two-dimensional (2-D) filters. The proposed structure has a minimun mumber of delay elements and multipliers. Based on this circuit realization, the corresponding state-space realization–representation is derived. The dimension of the 2-D state-space vector is minimal and the corresponding transfer function is ch...

We construct the Neveu-Schwarz sector of heterotic string field theory using the large Hilbert space of the superghosts and the multi-string products of bosonic closed string field theory. No picture-changing operators are required as in Wess-Zumino-Witten-like open superstring field theory. The action exhibits a novel kind of nonpolynomiality: in addition to terms necessary to cover missing re...

In this paper, we introduce operator s-convex functions and establish some Hermite-Hadamard type inequalities in which some operator s-convex functions of positive operators in Hilbert spaces are involved.

We consider the minimization of convex functionals on a real Hilbert space. The requisite theory is reviewed, and concise proofs of the relevant results are given.