A Nowhere Analytic C$^\infty$ Function

The improper infinite derivatives of Takagi’s nowhere-differentiable function

Let T be Takagi’s continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono [Acta Math. Hungar. 49 (1987)], we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the set...

An Analysis of Katsuura’s Continuous Nowhere Differentiable Function

Discrete Analytic Function

Galaxy Luminosity Function: A New Analytic Expression

We propose a new analytic approximation for the luminosity function of galaxies. The suggested expression behaves like the Schechter function at the faint end (φ ∼ L) but departs considerably at the bright end (L >> L∗). We argue here that such a behavior may provide a better fit for the current observational data than does the Schechter function. Its practical interest is stressed by consideri...

A Function-Analytic Development of Field Theory

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