Calculus on the Sierpinski Gasket I: Polynomials, Exponentials and Power Series

We study the analog of power series expansions on the Sierpinski gasket, for analysis based on the Kigami Laplacian. The analog of polynomials are multiharmonic functions, which have previously been studied in connection with Taylor approximations and splines. Here the main technical result is an estimate of the size of the monomials analogous to x^n/n!. We propose a definition of entire analytic functions as functions represented by power series whose coefficients satisfy exponential growth conditions that are stronger than what is required to guarantee uniform convergence. We present a characterization of these functions in terms of exponential growth conditions on powers of the Laplacian of the function. These entire analytic functions enjoy properties, such as rearrangement and unique determination by infinite jets, that one would expect. However, not all exponential functions (eigenfunctions of the Laplacian) are entire analytic, and also many other natural candidates, such as the heat kernel, do not belong to this class. Nevertheless, we are able to use spectral decimation to study exponentials, and in particular to create exponentially decaying functions for negative eigenvalues

Staging the ‘Forgotten Genocide’ in the Aftermath of the Dirty War: Una bestia en la luna by Richard Kalinoski

The most recent Argentine military dictatorship (1976-1983) and the Armenian Genocide (1915-1923) share legacies of state-sanctioned denial and impunity, which have left survivors and subsequent generations grappling with issues of memory and mourning. The intersection of these two collective memories in Argentina, home to a sizable Armenian population, offers a glimpse into how post-dictatorial and post-genocidal memory politics have borrowed from and shaped each other. This article examines the positive reception in Argentina of Una bestia en la luna by the U.S. playwright Richard Kalinoski. While the work treats the struggles of two survivors of the Armenian Genocide and sets its dramatic action in the U.S., Kalinoski’s use of photography to warn against the dangers of silencing memory engages non-Armenian spectators in postdictatorial Argentina