In 1934, Walsh noted that the Taylor polynomial of degree n can be obtained by taking the limit as {lunate} 0 + of the net of nth degree polynomials which best approximate f in the closed discs | z | {lunate}. Later, this result was generalized to rational approximation. In a recent paper, Shisha and the first two authors generalized this idea to the idea of best local approximation. In this paper, using a different technique, we study this problem in the L 2 setting. Consequently, better results follow under weaker hypotheses. 1978.
