1] The norm of the polynomial truncation operator on the unit disk and on [-1

2001, Instytut Matematycznys. All rights reserved. Let D and D denote the open unit disk and the unit circle of the complex plane, respectively. We denote by Pn (resp. Pcn) the set of all polynomials of degree at most n with real (resp. complex) coefficients. We define the truncation operators Sn for polynomials Pn Pcn of the form Pn(z) := nj=0, ajzj, by aj , by (Formula presented.) (here 0/0 is interpreted as 1). We define the norms of the truncation operators by (Formula presented.) Our main theorem establishes the right order of magnitude of the above norms: there is an absolute constant c1 > 0 such that (Formula presented.) This settles a question asked by S. Kwapie. Moreover, an analogous result in Lp(D) for p [2,] is established and the case when the unit circle D is replaced by the interval [1, 1] is studied.

The norm of the polynomial truncation operator on the unit disk and on [-1,1] Academic Article