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Regularity of domains of parameterized families of closed linear operators

100%

Winiarska T., Winiarski T.

Annales Polonici Mathematici

2003

tom 80

nr 1

231-241

The purpose of this paper is to provide a method of reduction of some problems concerning families $A_t = (A(t))_{t∈𝓣}$ of linear operators with domains $(𝓓_t)_{t∈𝓣}$ to a problem in which all the operators have the same domain 𝓓. To do it we propose to construct a family $(Ψ_t)_{t∈𝓣}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t ↦ Ψ_t$ is sufficiently regular and (ii) $Ψ_t(𝓓) = 𝓓_t$ for t ∈ 𝓣. Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition with a parameter; for operators in a Hilbert space for which eigenspaces form a complete orthogonal system of closed linear subspaces; and for a class of closed operators having bounded inverses.

A note on Bézout's theorem

81%

Rams S., Tworzewski P., Winiarski T.

Annales Polonici Mathematici

2005

tom 87

nr 1

219-227

We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Winiarski T.

1 Rams S.

1 Tworzewski P.

1 Winiarska T.

1 2005

1 2003

Wyniki wyszukiwania

Regularity of domains of parameterized families of closed linear operators

A note on Bézout's theorem