Fractal Zeta Functions at Infinity and the \(\phi \)-Shell Minkowski Content
摘要
We study fractal properties of unbounded domains with infinite Lebesgue measure via their complex fractal dimensions. These complex dimensions are defined as poles of a suitable defined Lapidus fractal zeta function at infinity and are a generalization of the Minkowski dimension for a special kind of a degenerated relative fractal drums at infinity. It is a natural generalization of a similar approach applied to unbounded domains of finite Lebesgue measures investigated previously by the author. In this case we adapt the definition of Minkowski content and dimension at infinity by introducing the so-called