Division subspaces and integrable kernels

In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.Comment: 11 page

Functional description of a class of quasi-invariant determinantal processes

We give a functional characterization of a class of quasi-invariant determinantal processes corresponding to projection kernels in terms of de Branges spaces of entire funcitons.Comment: 14 page

Electrically-Detected ESR in Silicon Nanostructures Inserted in Microcavities

We present the first findings of the new electrically-detected electron spin resonance technique (EDESR), which reveal the point defects in the ultra-narrow silicon quantum wells (Si-QW) confined by the superconductor delta-barriers. This technique allows the ESR identification without application of an external cavity, as well as a high frequency source and recorder, and with measuring the only response of the magnetoresistance, with internal GHz Josephson emission within frameworks of the normal-mode coupling (NMC) caused by the microcavities embedded in the Si-QW plane