Communications of the
Korean Mathematical Society CKMS

Generalized nonnegative polynomials are defined as the products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We extend some results on Infinite-Finite range inequalities, Christoffel functions, and Nikolski\u\i\ type inequalities corresponding to weights $W_\alpha(x)= \exp(-|x|^\alpha)$, $\alpha >0$, to those for generalized nonnegative polynomials.

Keywords: generalized polynomials, Infinite-Finite range inequalities, Christoffel functions, Nikolskiui type inequalities, exponential weights

MSC numbers: 41A17