László Máté

Budapest University of Technology and Economics · Department of Mathematical Analysis

lecture notes for an undergraduate level of a dynamical approach of fractal theory

no abstract

We give a necessary and sufficient condition for a certain set of infinite products of linear operators to be zero. We shall investigate also the case when this set of infinite products converges to a non-zero operator. The main device in these results is a weighted version of the König Lemma for infinite trees in graph theory.

is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any z ∈ R n and any σ = {σ 1 , σ 2 , . . .} belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every σ = {σ 1 , σ 2 , . . .} ∈ Σ the composition (1) is a contraction. Thi...

The König Lemma for infinite trees in Graph Theory says that in an infinite rooted tree with all vertices of finite degree, there is an infinite path starting from the root. In this weighted version we shall show that there is an infinite path with weights greater than a certain average. We shall apply our result to infinite compositions of affine...

We give a necessary and sufficient condition for a certain set of infinite products of linear operators to be zero. We investigate also the case when this set of infinite products converges to a non-zero operator. The main device in these results is a weighted version of the König lemma for infinite trees in graph theory.

The proof of Theorem 1 in the paper named in the title [ibid. 23, No. 1, 59-63 (1991; Zbl 0746.46005)] is corrected.

Thesis (doctoral)--Budapest, 1964.