Browsing by Subject "Smoothness"

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    On possible deterioration of smoothness under the operation of convolution
    (1996) Uludağ, A. Muhammed
    We show that the convolution of two probability densities which are restrictions to R of entire functions can possess infinite essential supremuin on each interval. We also present several sufficient conditions of deterioration of smoothness under the operation of convolution.
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    Smoothness properties of Green's functions
    (2014) Türkün, Can
    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 given. It is discussed that for what kind of sets they are continuous. Then, it is analyzed how good their continuity can be, how smooth they can be. Examples are given for the optimal smoothness. Besides, many other examples with diverse moduli of continuity are considered. Recent developments and articles in this field are introduced in details. Finally, an open problem about finding a Cantor type set K(γ) for preassigned smoothness of Green’s function is presented.