UNIQUENESS OF SOLUTIONS TO A 2-DIMENSIONAL MEAN PROBLEM Academic Article uri icon

abstract

  • Let 0 < rm < 1, rmm {variant} for all large m, and let wn = e i2 n, n = 1, 2, 4 For a function f{hook}(z) = anzn, holomorphic in the open unit disk U, let sn(f{hook}) = ( 1 n) k = 1nf{hook}(rnwnk), the nth arithmetic mean of f{hook} over the circle |z| = rn. We prove that if p < 1 and an = O(n-1) for 1 = 1.728..., then f{hook} is uniquely determined by the two-dimensional means sn(f{hook}), n = 1, 2, 4 We also prove that for each {variant}, 0 < {variant} < 1, there is a nontrivial f{hook}, holomorphic in U. such that sn(f{hook}) = 0 for n = 1, 2,... with rn = {variant} 1 n. 1978.

published proceedings

  • JOURNAL OF APPROXIMATION THEORY

author list (cited authors)

  • BOROSH, I., & CHUI, C. K.

citation count

  • 0

complete list of authors

  • BOROSH, I||CHUI, CK

publication date

  • January 1978