An important problem in analysis on fractals is the existence and the determination of an eigenform on a given finitely ramified fractal. It is known that on every fractal either with three vertices or with connected interior, an eigenform exists for suitable weights on the cells. In this paper, we prove that if the fractal has three vertices and connected interior, the form having all coefficients equal to 1 is an eigenform for suitable weights on the cells.
Elia, M., Peirone, R. (2018). EIGENFORMS on FRACTALS with CONNECTED INTERIOR and THREE VERTICES. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 26(4), 1850082 [10.1142/S0218348X18500822].
EIGENFORMS on FRACTALS with CONNECTED INTERIOR and THREE VERTICES
Elia M.;Peirone R.
2018-01-01
Abstract
An important problem in analysis on fractals is the existence and the determination of an eigenform on a given finitely ramified fractal. It is known that on every fractal either with three vertices or with connected interior, an eigenform exists for suitable weights on the cells. In this paper, we prove that if the fractal has three vertices and connected interior, the form having all coefficients equal to 1 is an eigenform for suitable weights on the cells.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
