Abstract:
In this paper, some solvability problems for functional equations of the form
F(t)−a1(t)F(δ1(t))−a2(t)F(δ2(t))=h(t),t∈I,F(t)−a1(t)F(δ1(t))−a2(t)F(δ2(t))=h(t),t∈I,
are studied. Here II is a finite closed interval in R, F is an unknown continuous function, δ1 and δ2 are given continuous maps of I into itself, and a1(t), a2(t), and h(t) are real-valued continuous functions on I. Such equations are of interest not only by themselves as an object of
analysis, but they are also a necessary link in solving various problems in such diverse fields as integral and functional equations, measure theory, and boundary problems for hyperbolic differential equations. The major part of the proofs is based on the new results in the theory of dynamical systems generated by a noncommutative semigroup with two generators.
Citation:
B. P. Paneah, “On Solvability of Functional Equations Relating to Dynamical Systems with Two Generators”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 55–72; Funct. Anal. Appl., 37:1 (2003), 46–60
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\by B.~P.~Paneah
\paper On Solvability of Functional Equations Relating to Dynamical Systems with Two Generators
\jour Funktsional. Anal. i Prilozhen.
\yr 2003
\vol 37
\issue 1
\pages 55--72
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\jour Funct. Anal. Appl.
\yr 2003
\vol 37
\issue 1
\pages 46--60
\crossref{https://doi.org/10.1023/A:1022924027277}
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This publication is cited in the following 11 articles:
B. Paneah, Springer Optimization and Its Applications, 68, Nonlinear Analysis, 2012, 525
Shalit O.M., “Conjugacy of P-configurations and nonlinear solutions to a certain conditional Cauchy equation”, Banach J. Math. Anal., 3:1 (2009), 28–35
Paneah B., “A new approach to the stability of linear functional operators”, Aequationes Mathematicae, 78:1–2 (2009), 45–61
Paneah B., “Identifying functions determined by linear functional operators”, Russ. J. Math. Phys., 15:2 (2008), 291–296
Paneah B., “Some remarks on stability and solvability of linear functional equations”, Banach J. Math. Anal., 1:1 (2007), 56–65
Zubelevich O., “A note on theorem of Massera”, Regul. Chaotic Dyn., 11:4 (2006), 475–481
Paneah B.P., “Dynamical systems and functional equations related to boundary problems for hyperbolic differential operators”, Dokl. Math., 72:3 (2005), 949–953
Paneah B., “Dynamical approach to some problems in integral geometry”, Trans. Amer. Math. Soc., 356:7 (2004), 2757–2780
Paneah B., “On the over determinedness of some functional equations”, Discrete Contin. Dyn. Syst., 10:1-2 (2004), 497–505
Paneah B., “Dynamic methods in the general theory of Cauchy type functional equations”, Complex Analysis and Dynamical Systems - Israel Mathematical Conference Proceedings, Contemporary Mathematics Series, 364, 2004, 205–223
Paneah B., “Noncommutative dynamical systems with two generators and their applications in analysis”, Discrete Contin. Dyn. Syst., 9:6 (2003), 1411–1422
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