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Numerical index with respect to an operator

100%

Ardalani M.

Studia Mathematica

2014

tom 225

nr 2

165-171

We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.

Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

63%

Ardalani M., Lusky W.

Studia Mathematica

2012

tom 209

nr 3

225-234

Let v be a standard weight on the upper half-plane 𝔾, i.e. v: 𝔾 → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ 𝔾, v(it) ≥ v(is) if t ≥ s > 0 and $lim_{t→ 0} v(it) = 0$. Put v₁(w) = Im wv(w), w ∈ 𝔾. We characterize boundedness and surjectivity of the differentiation operator D: Hv(𝔾) → Hv₁(𝔾). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv(𝔾).

Ograniczanie wyników

2 Studia Mathematica

2 Ardalani M.

1 Lusky W.

1 2014

1 2012

Wyniki wyszukiwania

Numerical index with respect to an operator

Bounded operators on weighted spaces of holomorphic functions on the upper half-plane