arXiv subjects
Publications and source records attributed to Ugur Gul.
This paper explores a version of the classical Ces\`{a}ro integral operator for the Lebesgue space $L^p(0, 1)$ where we discuss its norm, spectral properties, cyclicity, and invariant subspaces. The spectrum of the Ces\`{a}ro operator will be a crescent domain whose geometry depends on $p$. An important tool will be semigroups of weighted composition operators on $L^p(0, 1)$.
This paper explores a version of the classical Ces`aro integral operator for the Lebesgue space L2(0, 1) where we discuss its norm, adjoint, spectral properties, and invariant subspaces. An important tool will be semigroups of weighted composition operators on L2(0, 1).
In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as "quasi-parabolic". This is the class of composition operators on H^{2} with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form ϕ(z) = z+ψ(z) where ψ\in H^{2}(\mathbb{H}) and \Im(ψ(z)) >δ> 0. We especially examine the case where ψis discontinuous at infinity. A new method is devised to show that this type of composition operators fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra.