arXiv subjects

Athanasios G. Arvanitidis

Publications and source records attributed to Athanasios G. Arvanitidis.

3 recordsLinked to original sources

arXiv2016

The Quantization of the Rabi Hamiltonian

The Bargmann-Fock representation of the Rabi Hamiltonian is expressed by a system of two coupled first-order differential equations in the complex field, which may be rewritten in a canonical form under the Birkhoff transformation. The transformation gives rise to leapfrog recurrence relations, from which the eigenvalues and eigenvectors could be obtained. The interesting feature of this approach is that it generates integer quantum numbers, which relate the solutions to the Juddian baselines. The relationship with Braak's integrability claim [PRL 107, 100401 (2011)] is discussed

math-ph↗

arXiv2011

Semigroups of Composition Operators on Hardy Spaces of the half-plane

We identify the semigroups consisting of bounded composition operators on the Hardy spaces $H^p(\U)$ of the upper half-plane. We show that any such semigroup is strongly continuous on $H^p(\U)$ but not uniformly continuous and we identify the infinitesimal generator.

math.FA↗

arXiv2010

Cesaro operators on the Hardy spaces of the half-plane

In this article we study the Cesàro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(ζ)\,dζ, $$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as resolvents for appropriate semigroups of composition operators and we find the norm and the spectrum in each case. The relation of $\mathcal{C}$ and $\mathcal{T}$ with the corresponding Cesàro operators on Lebesgue spaces $L^p(\R)$ of the boundary line is also discussed.

math.CV↗