Browsing by Subject "Logarithmic dimension"

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    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].