We provide new estimates on the degree of Cl-G-determinacy (G is one of Mather’s groups R, C, or K) of weighted homogeneous map germs satisfying a convenient Lojasiewicz condition. The results give an explicit order such ...

There is a growing demand for food supplements containing high amounts of vitamins, phenolic compounds and mineral content that provide health benefits. Those functional compounds have different solubility properties, and ...

It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic ...

We introduce a concept of best local approximation using abstract norms and non-homogeneous dilations. The asymptotic behavior of the normalized error function as well as the limit of some net of best approximation polynomials ...

Current interest in health has led to an increase in demand for functional food supplements as well as in industry concern for maintaining the bioactive compounds of such foods via the application of new technologies. In ...

We obtain a comparison of the level sets for two maximal functions on a space of homogeneous type: the Hardy-Littlewood maximal function of mean values over balls and the dyadic maximal function of mean values over the ...

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are ...

In this note we investigate some basic properties of the level sets of functions which are homogeneous with respect to nonisotropic dilations. In particular we obtain a formula for the volume of the level sets in terms of ...