In the present paper we consider the nonlinear superposition operator F in Banach spaces of sequences l p (1 ≤ p ≤ ∞), generated by the function f (s, u) = d(s) + a ku − 1, with a > 1 and k ∈ R \ {0}. We find out the Rhodius spectra σ R (F) and the Neuberger spectra σ N (F) of these operators, depending on the values of k.
In this paper, we consider the topic from the theory of cosine operator functions in 2-dimensional real vector space, which is an interplay between functional analysis and matrix theory. For the various cases of a given real matrix A= [α , β; γ , δ] we find out the appropriate cosine operator function C(t)= [a(t), b(t); c(t), d(t)], (t \in R) in a real vector space R2 as the solutions of the Cauchy problem C''(t)=AC(t), C(0)=I, C'(0)=0.
In this paper, we consider the nonlinear superposition operator F in lp spaces of sequences (1 ≤ p ≤ ∞), generated by the function
f(s,u)=a(s) + arctan u or f(s,u) = a(s) - arctan u.
We find out the Rhodius spectra σR(F) and the Neuberger spectra σN(F) of these operators and finally the radii of these spectra. The superposition operator generated by the function f(s,u) = a(s) ∓ arccot u appears to be a special case of above mentioned operator.
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