Browsing by Subject "Whitney spaces"

Now showing 1 - 6 of 6

Open Access
Bases in banach spaces of smooth functions on cantor-type sets
(2013) Özfidan, Necip
We construct Schauder bases in the spaces of continuous functions C p (K) and in the Whitney spaces E p (K) where K is a Cantor-type set. Here different Cantortype sets are considered. In the construction, local Taylor expansions of functions are used. Also we show that the Schauder basis which we constructed in the space Cp(K), is conditional.
Open Access
Bases in some spaces of Whitney functions
(Duke University Press, 2017-06) Goncharov, Alexander; Ural, Zeliha
We construct topological bases in spaces of Whitney functions on Cantor sets, which were introduced by the first author. By means of suitable individual extensions of basis elements, we construct a linear continuous exten- sion operator, when it exists for the corresponding space. In general, elements of the basis are restrictions of polynomials to certain subsets. In the case of small sets, we can present strict polynomial bases as well.
Open Access
Existence of basis in some Whitney spaces
(2003) Keşir, Mustafa
Existence of basis in locally convex spaces has been a hot subject in functional analysis for more than 40 years. We will give some partial solutions to this well-known problem. We will demonstrate two cases of Cantor-type sets with extension property under some special cases. These sets are KN with (DN) where lim sup αn < N and K∞ with (DN) where lim sup αn < ∞.
Open Access
Logarithmic dimension and bases in Whitney spaces
(Scientific and Technical Research Council of Turkey - TUBITAK,Turkiye Bilimsel ve Teknik Arastirma Kurumu, 2021-07-27) Goncharov, Alexander; Şengül Tezel, Yasemin
We give a formula for the logarithmic dimension of the generalized Cantor-type set K . In the case when the logarithmic dimension of K is smaller than 1, we construct a Faber basis in the space of Whitney functions E(K).
Open Access
Logarithmic dimension and bases in whitney spaces
(2006) Şengül, Yasemin
In generalization of [3] we will give the formula for the logarithmic dimension of any Cantor-type set. We will demonstrate some applications of the logarithmic dimension in Potential Theory. We will construct a polynomial basis in E(K(Λ)) when the logarithmic dimension of a Cantor-type set is smaller than 1. We will show that for any generalized Cantor-type set K(Λ), the space E(K(Λ)) possesses a Schauder basis. Locally elements of the basis are polynomials. The result generalizes theorems 1 and 2 in [12].
Open Access
Quasi-equivalence of bases in some Whitney spaces
(Cambridge University Press, 2021-05-18) Goncharov, Alexander; Şengül, Yasemin
If the logarithmic dimension of a Cantor-type set K is smaller than 1 , then the Whitney space E(K) possesses an interpolating Faber basis. For any generalized Cantor-type set K, a basis in E(K) can be presented by means of functions that are polynomials locally. This gives a plenty of bases in each space E(K) . We show that these bases are quasi-equivalent.