The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in form of a composition characteristics used mathematical description control systems. This can be defined relative various orthonormal bases. For given deterministic square-integrable kernels, characteristic operator determined as an infinite random matrix. main applications such su...

We study a separability problem suggested by mathematical description of bipartite quantum systems. We consider Hermitian 2-forms on the tensor product H = K ⊗ L, where K, L are finite dimensional complex spaces. Inspired by quantum mechanical terminology we call such a form separable if it is a convex combination of hermitian tensor products σ * p ⊙ σ p of 1-forms σ p on H that are product for...

The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L(A) requires the existence of a square-integrable function whose Plancherel transform satisfies Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable funct...