Displaying similar documents to “On the existence of minimal hyperspheres in compact symmetric spaces”

Spectral localization, power boundedness and invariant subspaces under Ritt's type condition

Yu. Lyubich (1999)

Studia Mathematica

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For a bounded linear operator T in a Banach space the Ritt resolvent condition ∥ R λ ( T ) ∥ ≤ C / | λ - 1 | (|λ| > 1) can be extended (changing the constant C) to any sector |arg(λ - 1)| ≤ π - δ, a r c c o s ( C - 1 ) < δ < π / 2 . This implies the power boundedness of the operator T. A key result is that the spectrum σ(T) is contained in a special convex closed domain. A generalized Ritt condition leads to a similar localization result and then to a theorem on invariant subspaces.

On a certain map of a triangle

Grzegorz Świrszcz (1998)

Fundamenta Mathematicae

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The paper answers some questions asked by Sharkovski concerning the map F:(u,v) ↦ (u(4-u-v),uv) of the triangle Δ = u,v ≥ 0: u+v ≤ 4. We construct an absolutely continuous σ-finite invariant measure for F. We also prove the following strange phenomenon. The preimages of side I = Δ ∩ v=0 form a dense subset ∪ F - n ( I ) of Δ and there is another dense set Λ consisting of points whose orbits approach the interval I but are not attracted by I.

Rough maximal functions and rough singular integral operators applied to integrable radial functions.

Peter Sjögren, Fernando Soria (1997)

Revista Matemática Iberoamericana

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Let Ω be homogeneous of degree 0 in R and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor Ω in the definition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels Ω(y) / |y|, provided that the mean value of Ω vanishes. In an earlier paper, the authors showed that a two-dimensional rough maximal operator is of weak type (1,1) when restricted to radial functions. This result is now extended to...