In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod pow...In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.展开更多
Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note d...Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities under L^p norm for 0〈p≤∞. Our results essentially extend the result of Wang and Zhou （2002）, and the method used in this paper is simpler and more direct than that of Wang and Zhou （2002）. The results and methods have their own values in approximation theory and computation.展开更多
文摘In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.
文摘Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities under L^p norm for 0〈p≤∞. Our results essentially extend the result of Wang and Zhou （2002）, and the method used in this paper is simpler and more direct than that of Wang and Zhou （2002）. The results and methods have their own values in approximation theory and computation.
