On the Asymptotic Behavior of Solutions to General Linear Functional Equations

B. Paneah ()
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B. Paneah: Technion—Israel Institute of Technology

Chapter Chapter 33 in Nonlinear Analysis, 2012, pp 525-537 from Springer

Abstract: Abstract This is a survey of the author’s results (Paneah in Aequ. Math. 74(1–2):119–157, 2007; Paneah in Grazer Math. Ber. 351:129–138, 2007; Paneah in Banach J. Math. Anal. 1(1):56–65, 2007; Paneah in Russ. J. Math. Phys. 15(2):291–296, 2008; Paneah in Publ. Math. (Debr.) 75(1–2):251–261, 2009) relating to the asymptotic behavior of approximate solutions to the functional equations , H ε =O(ε), depending on a parameter ε→0 with This behavior, as it is shown in the above works, is described by the relation $$F=\varPhi +O(\varepsilon). $$ Here the function Φ does not depend on ε and belongs to the kernel of the one-dimensional functional operator (restriction of the operator to some one-dimensional submanifold Γ⊂D subject to determining).

Keywords: Linear functional equations; Asymptotic behavior; Functional operators; Inverse problems; 39Bxx; 62G20; 93D20 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3498-6_33

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