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Some classes of infinitely differentiable functions

G. S. Balashova (1999)

Mathematica Bohemica

For nonquasianalytical Carleman classes conditions on the sequences { M ^ n } and { M n } are investigated which guarantee the existence of a function in C J { M ^ n } such that u(n)(a) = bn,    bnKn+1Mn,    n = 0,1,...,    aJ. Conditions of coincidence of the sequences { M ^ n } and { M n } are analysed. Some still unknown classes of such sequences are pointed out and a construction of the required function is suggested. The connection of this classical problem with the problem of the existence of a function with given trace at the boundary...

Some Coefficient Estimates for Polynomials on the Unit Interval

Qazi, M. A., Rahman, Q. I. (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.In this paper we present some inequalities about the moduli of the coefficients of polynomials of the form f (x) : = еn = 0nan xn, where a0, ј, an О C. They can be seen as generalizations, refinements or analogues of the famous inequality of P. L. Chebyshev, according to which |an| Ј 2n-1 if | еn = 0n an xn | Ј 1 for -1 Ј x Ј 1.

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