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On principal iteration semigroups in the case of multiplier zero

Dorota KrassowskaMarek Zdun — 2013

Open Mathematics

We collect and generalize various known definitions of principal iteration semigroups in the case of multiplier zero and establish connections among them. The common characteristic property of each definition is conjugating of an iteration semigroup to different normal forms. The conjugating functions are expressed by suitable formulas and satisfy either Böttcher’s or Schröder’s functional equation.

A pair of linear functional inequalities and a characterization of L p -norm

Dorota KrassowskaJanusz Matkowski — 2005

Annales Polonici Mathematici

It is shown that, under some general algebraic conditions on fixed real numbers a,b,α,β, every solution f:ℝ → ℝ of the system of functional inequalities f(x+a) ≤ f(x)+α, f(x+b) ≤ f(x)+β that is continuous at some point must be a linear function (up to an additive constant). Analogous results for three other similar simultaneous systems are presented. An application to a characterization of L p -norm is given.

When ( E , σ ( E , E ' ) ) is a D F -space?

Dorota KrassowskaWiesƚaw Śliwa — 1992

Commentationes Mathematicae Universitatis Carolinae

Let ( E , t ) be a Hausdorff locally convex space. Either ( E , σ ( E , E ' ) ) or ( E ' , σ ( E ' , E ) ) is a D F -space iff E is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].

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