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Currently displaying 1 – 2 of 2

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A geometric proof of the Perron-Frobenius theorem.

Alberto Borobia; Ujué R. Trías — 1992

Revista Matemática de la Universidad Complutense de Madrid

We obtain an elementary geometrical proof of the classical Perron-Frobenius theorem for non-negative matrices A by using the Brouwer fixed-point theorem and by studying the dynamics of the action of A on convenient subsets of Rn.

The dimension function of holomorphic spaces of a real submanifold of an almost complex manifold

Fernando Etayo; Mario Fioravanti; Ujué R. Trías — 2001

Czechoslovak Mathematical Journal

Let $M$ be a real submanifold of an almost complex manifold $(\bar{M}, \bar{J})$ and let $H_{x} = T_{x} M \cap \bar{J} (T_{x} M)$ be the maximal holomorphic subspace, for each $x \in M$ . We prove that $c M \to ℕ$ , $c (x) = {dim}_{ℝ} H_{x}$ is upper-semicontinuous.

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