2003
DOI: 10.3934/dcds.2003.9.1411
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Noncommutative dynamical systems with two generators and their applications in analysis

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Cited by 4 publications
(5 citation statements)
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“…The proof of this lemma coincides with the proof of Lemma 12 with the only exception: the reference to the maximum principle should be replaced by the reference to Theorem 1 in [5]. The corresponding assertion in [5] To prove the necessity of hypothesis (6) assume that…”
Section: Proof Of Part (Ii)mentioning
confidence: 83%
“…The proof of this lemma coincides with the proof of Lemma 12 with the only exception: the reference to the maximum principle should be replaced by the reference to Theorem 1 in [5]. The corresponding assertion in [5] To prove the necessity of hypothesis (6) assume that…”
Section: Proof Of Part (Ii)mentioning
confidence: 83%
“…The dynamical systems and all accompanying notions including the orbits we apply throughout this work were introduced for the first time in [4] and carefully studied in [8]. These notions have nothing in common with the classical dynamical systems and the orbits, first of all, because the semigroups of maps generating the new dynamical systems are generated by two maps but not one as in the classical situation.…”
Section: Discussionmentioning
confidence: 99%
“…Some confirmations of this fact the reader will find in Sec. 4. It turns out that an essential information related to the solvability of equation (0.1), especially, in the case of a P-configuration, may be derived by means of new dynamical methods, introduced in the author's paper [8]. The application of these methods becomes possible, if we associate this equation with a noncommutative semigroup of maps from the interval I into itself, generated by α 1 and α 2 .…”
Section: Figures 1 and 2 (See Below)mentioning
confidence: 99%
See 1 more Smart Citation
“…In this subsection we describe the results related to the unique solvability of the functional equation F( 1 (t) + 2 (t)) ; F( 1 (t)) ; F( 2 (t)) = H(t) t 2 I (8) in the case when the functions 1 (t) a n d 2 (t) f o r m a P -con guration and satisfy a (9) Due to hypotheses (7) and (9) form a P -con guration on I and in addition satisfy the condition 1 (t) + 2 (t) = t t 2 I: (10) Thus the ch a n g e o f v ariable t ! ;1 (t) reduces equation (1) (11) with a semigroup of maps in I, generated by 1 and 2 .…”
mentioning
confidence: 99%