We investigate the concepts of linear convexity and C-convexity in complex Banach spaces. The main result is that any C-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given a C-convex domain Ω in the Banach space X and a point p / ∈Ω, there is a complex hyperplane through p that does not intersect Ω. We also prov...

We prove some decay estimates of the energy of the wave equation governed by localized nonlinear dissipations in a bounded domain in which trapped rays may occur. The approach is based on a comparison with the linear damped wave equation and an interpolation argument. Our result extends to the nonlinear damped wave equation the well-known optimal logarithmic decay rate for the linear damped wav...

A new method for modeling functions that intersect given points is developed and demonstrated. This method yields a generally non-Gaussian probability density of y given x that has properties which are often desired in practice. It is shown that this density can have a smoother mean function and a variance which is never larger than that of a classic Gaussian process density.

We study Rubin’s variant of the p-adic Birch and Swinnerton-Dyer conjecture for CM elliptic curves concerning certain special values of the Katz two-variable p-adic L-function that lie outside the range of p-adic interpolation.

This paper proves lower bounds for the eigenvalues of positive definite matrices arising from interpolation of scattered data by positive definite kernels. By comparison with upper bounds for the interpolation error, it turns out that both bounds are asymptotically optimal for sufficiently dense data sets. Applications include interpolation on the sphere, the torus, and general Riemannian manif...

In this paper, we survey recent developments in the birational geometry of the moduli spaces M(ξ) of semistable sheaves on P following [ABCH], [CH], [CH2], [CHW] and [H]. We discuss the cones of effective, ample and movable divisors on M(ξ). We introduce Bridgeland stability conditions, the main technical tools that precipitated the recent advances, and explain their applications to interpolati...

If the sequence a = (a„>^ E /2, i.e., ||a||2 = 2~=0 | a„ |2 < oo, define Sa as the sequence of averages 1 " 2 ak n + 1 , It follows easily from the Marcinkiewicz Interpolation Theorem that S is a bounded operator from I2 to I2; this can also be proved directly using the Cauchy-Buniakowski-Schwarz inequality [1]. S is known as the Cesàro operator. S is, of course, not bounded below, but the foll...

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more precise result using the real interpolation theory and we clarify the use of Hardy spaces. Then with the help of the bilinear interpolation theory, we then give ap...

We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.