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Now showing items 114 of 14

Approximation of equilibrium measures by discrete measures
(Bilkent University, 2012)Basic notions of potential analysis are given. Equilibrium measures can be approximated by discrete measures by means of Fekete points and Leja sequences. We give the sets for which exact locations of Fekete points and ... 
Bases in banach spaces of smooth functions on cantortype sets
(Bilkent University, 2013)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 Cantortype set. Here different Cantortype sets are considered. In the construction, local ... 
Consistency in house allocation problems
(Bilkent University, 1999) 
Extension operators for spaces of infinitely differentiable functions
(Bilkent University, 2005)We start with a review of known linear continuous extension operators for the spaces of Whitney functions. The most general approach belongs to PawÃlucki and Ple´sniak. Their operator is continuous provided that the ... 
Extension problem and bases for spaces of infinitely differentiable functions
(Bilkent University, 201704)We examine the Mityagin problem: how to characterize the extension property in geometric terms. We start with three methods of extension for the spaces of Whitney functions. One of the methods was suggested by B. S. Mityagin: ... 
Geometric characterization of extension property for model compact sets
(Bilkent University, 2000) 
Interpolating bases in the spaces of C(formula)functions on cantortype sets
(Bilkent University, 2006)In this work by using the method of local interpolat ions suggested in [9] we construct topological bases in the spaces of CPfunctions defined on uniformly perfect compact sets of Cantor type. Elements of the basis are ... 
Lebesgue constants on cantor type sets
(Bilkent University, 202009)The properties of compact subsets of the real line which are in the class of Bounded Lebesgue Constants (BLC) are investigated. Knowing that any such set must have 1dimensional Lebesgue measure zero and nowhere density, ... 
Linear topological structure of spaces of Whitney functions defined on sequences of points
(Bilkent University, 2002)In this work we consider the spaces of Whitney functions defined on convergent sequences of points.By means of linear topological invariants we analyze linear topological structure of these spaces .Using diametral dimension ... 
Logarithmic dimension and bases in whitney spaces
(Bilkent University, 2006)In generalization of [3] we will give the formula for the logarithmic dimension of any Cantortype set. We will demonstrate some applications of the logarithmic dimension in Potential Theory. We will construct a polynomial ... 
Numerical study of orthogonal polynomials for fractal measures
(Bilkent University, 201607)In recent years, potential theory has an essential effect on approximation theory and orthogonal polynomials. Basic concepts of the modern theory of general orthogonal polynomials are described in terms of Potential Theory. ... 
Smoothness of the green function for some special compact sets
(Bilkent University, 2010)Smoothness of the Green functions for some special compact sets, which are sequences of closed intervals with certain parameters, is described in terms of the function ϕ(δ) = 1 log 1 δ that gives the logarithmic measure ... 
Smoothness properties of Green's functions
(Bilkent University, 2014)Basic notions of potential theory are explained with illustrative examples. Many important properties, including the characteristic ones, of Green’s functions that are defined by the help of equilibrium measures are ... 
Widom Factors
(Bilkent University, 2014)In this thesis we recall classical results on Chebyshev polynomials and logarithmic capacity. Given a nonpolar compact set K, we define the nth Widom factor Wn(K) as the ratio of the supnorm of the nth Chebyshev ...