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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 1, Pages 55–72 (Mi faa136)  

This article is cited in 10 scientific papers (total in 10 papers)

On Solvability of Functional Equations Relating to Dynamical Systems with Two Generators

B. P. Paneah

Technion – Israel Institute of Technology

Abstract: In this paper, some solvability problems for functional equations of the form
$$ F(t)-a_1(t)F(\delta_1(t))-a_2(t)F(\delta_2(t))=h(t),\qquad t\in I, $$
are studied. Here $I$ is a finite closed interval in $\mathbb{R}$, $F$ is an unknown continuous function, $\delta_1$ and $\delta_2$ are given continuous maps of $I$ into itself, and $a_1(t)$, $a_2(t)$, 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.

Keywords: dynamical system, orbit, functional equation, boundary problem, hyperbolic differential equation


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English version:
Functional Analysis and Its Applications, 2003, 37:1, 46–60

Bibliographic databases:

UDC: 517.965+517.938
Received: 27.01.2002

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

Citation in format AMSBIB
\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
\jour Funct. Anal. Appl.
\yr 2003
\vol 37
\issue 1
\pages 46--60

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    This publication is cited in the following articles:
    1. Paneah B., “Noncommutative dynamical systems with two generators and their applications in analysis”, Discrete Contin. Dyn. Syst., 9:6 (2003), 1411–1422  crossref  mathscinet  zmath  isi  scopus
    2. Paneah B., “Dynamical approach to some problems in integral geometry”, Trans. Amer. Math. Soc., 356:7 (2004), 2757–2780  crossref  mathscinet  zmath  isi  scopus
    3. Paneah B., “On the over determinedness of some functional equations”, Discrete Contin. Dyn. Syst., 10:1-2 (2004), 497–505  crossref  mathscinet  zmath  isi
    4. 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  crossref  mathscinet  zmath  isi
    5. Paneah B.P., “Dynamical systems and functional equations related to boundary problems for hyperbolic differential operators”, Dokl. Math., 72:3 (2005), 949–953  mathnet  mathscinet  zmath  isi  elib
    6. Zubelevich O., “A note on theorem of Massera”, Regul. Chaotic Dyn., 11:4 (2006), 475–481  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Paneah B., “Some remarks on stability and solvability of linear functional equations”, Banach J. Math. Anal., 1:1 (2007), 56–65  crossref  mathscinet  zmath  isi  scopus
    8. Paneah B., “Identifying functions determined by linear functional operators”, Russ. J. Math. Phys., 15:2 (2008), 291–296  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. 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  crossref  mathscinet  zmath  isi  scopus
    10. Paneah B., “A new approach to the stability of linear functional operators”, Aequationes Mathematicae, 78:1–2 (2009), 45–61  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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