The Full Mntz Theorem in C[0, 1] and L1[0, 1] Academic Article uri icon


  • The main result of this paper is the establishment of the 'full Mntz Theorem' in C[0, 1]. This characterizes the sequences {i}i = 1 of distinct, positive real numbers for which span {1, x1, x2, . . .} is dense in C[0, 1]. The novelty of this result is the treatment of the most difficult case when infi1 = 0 while supii = . The paper settles the L and L1 cases of the following. THEOREM (Full Mntz Theorem in Lp[0,1]). Let p[1, ]. Suppose that {i}i = 0 is a sequence of distinct real numbers greater than -1/p. Then span {x0, x1, . . .} is dense in Lp[0,1] if and only if (Formula presented).

published proceedings

  • Journal of the London Mathematical Society

author list (cited authors)

  • Borwein, P., & Erdlyi, T.

citation count

  • 25

complete list of authors

  • Borwein, Peter||Erdélyi, Tamás

publication date

  • August 1996