Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Markov's property for kth derivative

100%

Baran M., Milówka B., Ozorka P.

Annales Polonici Mathematici

2012

tom 106

nr 1

31-40

Consider the normed space $(ℙ(ℂ^{N}),||·||)$ of all polynomials of N complex variables, where || || a norm is such that the mapping $L_{g}: (ℙ(ℂ^{N}),||·||) ∋ f ↦ gf ∈ (ℙ(ℂ^{N}),||·||)$ is continuous, with g being a fixed polynomial. It is shown that the Markov type inequality $|∂/∂z_{j} P|| ≤ M(deg P)^{m} ||P||$, j = 1,...,N, $P ∈ ℙ(ℂ^{N})$, with positive constants M and m is equivalent to the inequality $||∂^{N}/∂z₁...∂z_{N} P|| ≤ M'(deg P)^{m'}||P||$, $P ∈ ℙ(ℂ^{N})$, with some positive constants M' and m'. A similar equivalence result is obtained for derivatives of a fixed order k ≥ 2, which can be more specifically formulated in the language of normed algebras. In addition, we give a nontrivial example of Markov's inequality in the Wiener algebra of absolutely convergent trigonometric series and show that the Banach algebra approach to Markov's property furnishes new tools in the study of polynomial inequalities.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Baran M.

1 Milówka B.

1 Ozorka P.

1 2012

Wyniki wyszukiwania

Markov's property for kth derivative