The inversion theorem and Plancherel's theorem in infinite dimensions

Inversion theorem and Plancherels theorem in Banach spac

On Polyharmonic Interpolation

In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from $C^{\infty}$ or analytic functions in the ball $B_{R}.$ We prove two main results on the interpolation of $C^{\infty}$ or analytic functions $f$ in the ball $B_{R}$ by polyharmonic functions $h$ of a given order of polyharmonicity $p.

The positive and negative consequences of stressors during early life

We discuss the long-term effects of stress exposure in pre- and early postnal life. We present an evolutionary framework within which such effects can be viewed, and describe how the outcomes might vary with species life histories. We focus on stressors that induce increases in glucocorticoid hormones and discuss the advantages of an experimental approach. We describe a number of studies demonstrating how exposure to these hormones in early life can influence stress responsiveness and have substantial long-term, negative consequences for adult longevity. We also describe how early life exposure to mild levels of stressors can have beneficial effects on resilience to stress in later life, and discuss how the balance of costs and benefits is likely dependent on the nature of the adult environment