Author(s)

Zaicun Li

Corresponding Author

Zaicun Li

ABSTRACT

The calculation method of the resistance between two points on an infinite grid has attracted many mathematicians for its promising engineering application. To calculate the resistance, the voltage function on the infinite grid should be calculated first given the current flowing in and out. The voltage function is a potential energy function, indicating that the choice of its zero point for a certain case is troublesome. In this paper, we consider the infinite network and define the voltage function in the space . Then we prove that the proposed voltage function is a pointwise limit and a limit in norm in another space

KEYWORDS

Resistance, Infinite network, Convergence in operator topology