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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

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

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

DOI: https://doi.org/10.4213/faa136

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

Bibliographic databases:

UDC: 517.965+517.938

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
\Bibitem{Pan03} \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 \mathnet{http://mi.mathnet.ru/faa136} \crossref{https://doi.org/10.4213/faa136} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1988009} \zmath{https://zbmath.org/?q=an:1029.39022} \transl \jour Funct. Anal. Appl. \yr 2003 \vol 37 \issue 1 \pages 46--60 \crossref{https://doi.org/10.1023/A:1022924027277} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182147400005} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0037252236} 

• http://mi.mathnet.ru/eng/faa136
• https://doi.org/10.4213/faa136
• http://mi.mathnet.ru/eng/faa/v37/i1/p55

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Paneah B., “Dynamical approach to some problems in integral geometry”, Trans. Amer. Math. Soc., 356:7 (2004), 2757–2780
3. Paneah B., “On the over determinedness of some functional equations”, Discrete Contin. Dyn. Syst., 10:1-2 (2004), 497–505
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
5. Paneah B.P., “Dynamical systems and functional equations related to boundary problems for hyperbolic differential operators”, Dokl. Math., 72:3 (2005), 949–953
6. Zubelevich O., “A note on theorem of Massera”, Regul. Chaotic Dyn., 11:4 (2006), 475–481
7. Paneah B., “Some remarks on stability and solvability of linear functional equations”, Banach J. Math. Anal., 1:1 (2007), 56–65
8. Paneah B., “Identifying functions determined by linear functional operators”, Russ. J. Math. Phys., 15:2 (2008), 291–296
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
10. Paneah B., “A new approach to the stability of linear functional operators”, Aequationes Mathematicae, 78:1–2 (2009), 45–61
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