Abstract In this paper we consider spaces of weight square-integrable and harmonic functions L 2 H (Ω, µ ). Weights for which there exists reproducing kernel ) are named ’admissible weights’ such kernels ’harmonic Bergman kernels’. We prove that if only integration is integrable in some negative power, then it admissible. Next construct a on the unit circle non-admissible using Bell-Ligocka the...

For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman...

We give a necessary and a sufficient condition for the boundedness of the Toeplitz product TF TG∗ on the vector valued Bergman space L 2 a(C ), where F and G are matrix symbols with scalar valued Bergman space entries. The results generalize those in the scalar valued Bergman space case [4]. We also characterize boundedness and invertibility of Toeplitz products TF TG∗ in terms of the Berezin t...

The immiscible displacement of oil by water through a porous and permeable reservoir rock can be described by the use of a fractional flow curves (fw versus Sw). Water flooding project parameters can be obtained from the fractional flow curve. However, developing a representative fractional flow curve for a specific reservoir can be quite challenging when fluid and special core analysis data is...

During the flood development in an oil field, the creep characteristic of mudstone is one of the important factors causing casing damage. In this study, based on the theory of fractional order differential and taking into account the creep damage evolution rules, a fractional nonlinear creep-damage model is proposed to reflect the instantaneous deformation in loading processes and the accelerat...