Local one-sided porosity and pretangent spaces

Altınok, Maya; Dovgoshey, Oleksiy; Küçükaslan, Mehmet

doi:10.1515/anly-2015-0011

Cited by 5 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(See, for example, [1, Corollary 5.5]). Similarly, from p − (X, x 0 ) > 1 2 it follows that [x 0 − ε, x 0 ) ∩ X = ∅ for some ε > 0. Hence, (2.13) implies that all points of X are isolated.…”

Section: Introductionmentioning

confidence: 91%

Boundedness of Lebesgue Constants and Interpolating Faber Bases

Bilet

Dovgoshey

Prestin

2017

Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"

View full text Add to dashboard Cite

Background. We investigate the relationship between the boundedness of Lebesgue constants for the Lagrange polynomial interpolation on a compact subset of  and the existence of a Faber basis in the space of continuous functions on this compact set. Objective. The aim of the paper is to describe the conditions on the matrix of interpolation nodes under which the interpolation of any continuous function coincides with the decomposition of this function in a series on the Faber basis. Methods. The methods of general theory of Schauder bases and the results which describe the convergence of interpolating Lagrange processes are used. Results. The structure of matrices of interpolation nodes which generate the interpolating Faber bases is described. Conclusions. Every interpolating Faber basis is generated by the interpolating Lagrange process with the interpolating matrix of a special kind and bounded Lebesgue constants.

show abstract

Section: Introductionmentioning

confidence: 91%

Boundedness of Lebesgue Constants and Interpolating Faber Bases

Bilet

Dovgoshey

Prestin

2017

Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"

View full text Add to dashboard Cite

show abstract

“…The standard definition of porosity at a finite point can be found in [26]. See [2,6,7,12] for some applications of the porosity to studies of the infinitesimal properties of metric spaces.…”

Section: Gluing Pretangent Spacesmentioning

confidence: 99%

On equivalence of unbounded metric spaces at infinity

Bilet¹,

Dovgoshey²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Let (X, d) be an unbounded metric space. To investigate the asymptotic behavior of (X, d) at infinity, one can consider a sequence of rescaling metric spaces (X, 1 rn d) generated by given sequence (r n ) n∈N of positive reals with r n → ∞. Metric spaces that are limit points of the sequence (X, 1 rn d) n∈N will be called pretangent spaces to (X, d) at infinity. We found the necessary and sufficient conditions under which two given unbounded subspaces of (X, d) have the same pretangent spaces at infinity. In the case when (X, d) is the real line with Euclidean metric, we also describe all unbounded subspaces of (X, d) isometric to their pretangent spaces.

show abstract

“…The sets E ⊆ R + with p(E) = 0 will be called lower nonporous at 0. It should be noted that p(E) > 1 2 holds if and only if 0 / ∈ E − {0} (See, for example, Corollary 5.5 in [1]). It does not therefore make sense to introduce the concept of strongly lower porous at 0 sets.…”

Section: The Lower Porosity At Zeromentioning

confidence: 99%

Unions and ideals of locally strongly porous sets

Altınok¹,

Dovgoshey²,

Küçükaslan³

2017

Turk J Math

Self Cite

View full text Add to dashboard Cite

For subsets of R + = [0, ∞) we introduce a notion of coherently porous sets as the sets for which the upper limit in the definition of porosity at a point is attained along the same sequence. We prove that the union of two strongly porous at 0 sets is strongly porous if and only if these sets are coherently porous. This result leads to a characteristic property of the intersection of all maximal ideals contained in the family of strongly porous at 0 subsets of R + . It is also shown that the union of a set A ⊆ R + with arbitrary strongly porous at 0 set is porous at 0 if and only if A is lower porous at 0 .

show abstract

Local one-sided porosity and pretangent spaces

Cited by 5 publications

References 13 publications

Boundedness of Lebesgue Constants and Interpolating Faber Bases

Boundedness of Lebesgue Constants and Interpolating Faber Bases

On equivalence of unbounded metric spaces at infinity

Unions and ideals of locally strongly porous sets

Contact Info

Product

Resources

About