23 research outputs found
Feynman integrals for non-smooth and rapidly growing potentials
The Feynman integral for the Schrödinger propagator is constructed as a generalized
function of white noise, for a linear space of potentials spanned by finite
signed measures of bounded support and Laplace transforms of such measures,
i.e., locally singular as well as rapidly growing at infinity. Remarkably, all these
propagators admit a perturbation expansion
Unified -deformation of one-parametric q-deformed oscillator algebras
We define a generalized -deformed oscillator
algebra and study the number of its characteristics. We describe the structure
function of deformation, analyze the classification of irreducible
representations and discuss the asymptotic spectrum behaviour of the
Hamiltonian. For a special choice of the deformation parameters we construct
the deformed oscillator with discrete spectrum of its "quantized coordinate"
operator. We establish its connection with the (generalized) discrete Hermite I
polynomials
Global robust exponential synchronization of BAM recurrent FNNs with infinite distributed delays and diffusion terms on time scales
Spectral theory and Wiener-Ito decomposition for the image of a Jacobi field
Assume that K: H → T is a bounded operator, where H and T are Hilbert spaces and ρ is a measure on the space H. Denote by ρ the image of the measure ρ under K . We study the measure ρ under the assumption that ρ is the spectral measure of a Jacobi field and obtain a family of operators whose spectral measure is equal to ρ. We also obtain an analog of the Wiener-Itô decomposition for ρ. Finally, we illustrate the results obtained by explicit calculations carried out for the case, where ρ is a Lévy noise measure