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On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
Georgian Mathematical Journal, 2008Abstract In the present paper we obtain both the pointwise convergence and the rate of pointwise convergence theorems of a class of operators defined by as (𝑥,λ) → (𝑥0,λ 0) in 𝐿1 〈𝑎,𝑏〉, where 〈𝑎,𝑏〉 is an arbitrary interval in 𝑅.
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Asymptotic Properties for Inhomogeneous Iterations of Nonlinear Operators
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On Modal Properties of the Koopman Operator for Nonlinear Systems with Symmetry
2019 American Control Conference (ACC), 2019This paper explores how symmetry in nonlinear dynamical systems is reflected in the modal properties of the corresponding Koopman operator. We first observe that symmetry in the dynamics is reflected in the symmetry of the Koopman eigenfunctions, as well as presence of repeated Koopman eigenvalues.
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Properties of Linear and Nonlinear Operators
2012In this section we point out some fundamental properties of linear operators in Banach spaces. The key assertions presented are the Uniform Boundedness Principle, the Banach–Steinhaus Theorem, the Open Mapping Theorem, the Hahn–Banach Theorem, the Separation Theorem, the Eberlain–Smulyan Theorem and the Banach Theorem.
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