We continue our recent study on constructing a refinement kernel for a given kernel so that the reproducing kernel Hilbert space associated with the refinement kernel contains that with the original kernel as a subspace. To motivate this study, we first develop a refinement kernel method for learning, which gives an efficient algorithm for updating a learning predictor. Several characterization...

We study the geometry of geodesics on $$\mathsf {SL}(n)$$ , equipped with Hilbert–Schmidt metric which makes it a Riemannian manifold. These are known to be related affine motions incompressible ideal fluids. The $$n = 2$$ case is special and completely integrable, geodesic motion was described by Roberts, Shkoller, Sideris; when 3$$ Sideris demonstrated some interesting features dynamics analy...

We consider the elementary operator L, acting on the Hilbert-Schmidt Class C2(H), given by L(T ) = ATB, with A and B bounded operators on a separable Hilbert space H. In this paper we establish results relating isometric properties of L with those of the defining symbols A and B. We also show that if A is a strict n−isometry on a Hilbert space H then {I, A∗A, (A∗)2A2, . . . , (A∗)n−1An−1} is a ...

Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G × G. These transforms have remarkable properties...

The aim of this paper is to give a precise proof the completeness Lamb modes and associated modes. This relatively simple short but relies on two powerful mathematical theorems. first one theorem elliptic systems with parameter due Agranovich Vishik. second Locker which gives criterion show set generalized eigenvectors Hilbert-Schmidt discrete operator.

Abstract We analyze the geometry on space of non-unital phase-covariant qubit maps. Using corresponding Choi-Jamiołkowski states, we derive Hilbert-Schmidt line and volume elements using channel eigenvalues together with parameter that characterizes non-unitality. find shapes analytically compute volumes channels, in particular entanglement breaking obtainable time-local generators.