Fractional powers of operators, K-functionals, Ulyanov inequalities

• Autorzy: Walter Trebels , Ursula Westphal
• Języki publikacji: EN

Abstrakty

EN

Given an equibounded (𝓒₀)-semigroup of linear operators with generator A on a Banach space X, a functional calculus, due to L. Schwartz, is briefly sketched to explain fractional powers of A. Then the (modified) K-functional with respect to $(X,D((-A)^α))$, α > 0, is characterized via the associated resolvent R(λ;A). Under the assumption that the resolvent satisfies a Nikolskii type inequality, $||λR(λ;A)f||_Y ≤ cφ(1/λ)||f||_X$, for a suitable Banach space Y, an Ulyanov inequality is derived. This will be of interest if one has good control on the resolvent but not on the semigroup.

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 46B70: Interpolation between normed linear spaces
• 47D60: C -semigroups, regularized semigroups
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 88
• Numer: 1
• Strony: 273-283

Daty

wydano

2010

Twórcy

autor

Walter Trebels

• AG 5, Fb. Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany

autor

Ursula Westphal

• Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

Identyfikatory

DOI

10.4064/bc88-0-22