We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate non-smooth functions. In such a case one usually expects the rate of approximation to be lower than that of smooth functions. It is shown in this paper that prior knowledge of the type of ’singularity’ of the function can be used to regain the full approximation power of the ...

based on the current approach, to ascertain and enforce the sanctions in law is one of the exclusive functions of governments. but the deeper examination reveals that many transactors prefer non-legal sanctions. at first glance, this self-enforcement mechanism seems to be contrary to legal fundamentals. therefore, these sanctions are contested in law. this article is an attempt to consider a ne...

We are concerned with the existence of smooth time functions on connected time–oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just defined a field of tangent convex cones (Cx)x∈M enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on ...

Maximally Smooth Functions (MSFs) are a form of constrained functions in which there no inflection points or zero crossings high order derivatives. Consequently, they have applications to signal recovery experiments where signals interest expected be non-smooth features masked by larger smooth foregrounds. They can also act as powerful tool for diagnosing the presence systematics. The nature MS...

The space c0 lies at the heart of many constructions of higher order smooth functions on Banach spaces. To name a few, recall Torunczyk’s proof of the existence of C-smooth partitions of unity on WCG spaces ([12]) or Haydon’s recent constructions of C-bump functions on certain C(K) spaces ([7]). The crucial property of c0 that allows for those constructions is a rich supply of C -smooth functio...

In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability, D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipsc...