Search results for "Bohr radius"
showing 7 items of 7 documents
The Bohr Radius of a Banach Space
2009
Following the scalar-valued case considered by Djakow and Ramanujan (A remark on Bohr’s theorem and its generalizations 14:175–178, 2000) we introduce, for each complex Banach space X and each \(1\le p0\). We study the p-Bohr radius of the Lebesgue spaces \(L^q(\mu )\) for different values of p and q. In particular we show that \(r_p(L^q(\mu ))=0\) whenever \(p<2\) and \(dim(L^q(\mu ))\ge 2\) and \(r_p(L^q(\mu ))=1\) whenever \(p\ge 2\) and \(p'\le q\le p\). We also provide some lower estimates for \(r_2(L^q(\mu ))\) for the values \(1\le q<2\).
The Dirichlet-Bohr radius
2015
[EN] Denote by Ω(n) the number of prime divisors of n ∈ N (counted with multiplicities). For x ∈ N define the Dirichlet-Bohr radius P L(x) to be the best r > 0 such that for every finite Dirichlet polynomial n≤x ann −s we have X n≤x |an|r Ω(n) ≤ sup t∈R X n≤x ann −it . We prove that the asymptotically correct order of L(x) is (log x) 1/4x −1/8 . Following Bohr’s vision our proof links the estimation of L(x) with classical Bohr radii for holomorphic functions in several variables. Moreover, we suggest a general setting which allows to translate various results on Bohr radii in a systematic way into results on Dirichlet-Bohr radii, and vice versa
Bohr radii of vector valued holomorphic functions
2012
Abstract Motivated by the scalar case we study Bohr radii of the N -dimensional polydisc D N for holomorphic functions defined on D N with values in Banach spaces.
Lateral induced dipole moment and polarizability of excitons in a ZnO single quantum disk
2013
The lateral Stark shift of an exciton confined in a single ZnO quantum thin disk of radius R was calculated using a variational approach within the two bands effective mass approximation. It is shown that the exciton has a non negligible induced dipole moment when an external electric field is applied mainly for electron-hole separation below to the 3D excitonic Bohr radius. The behavior of the exciton lateral Stark shift proves the existence of an important correlation between the polarizability and the induced dipole moment.
Theg-factor of highly charged ions
2015
Highly charged ions provide a unique opportunity to test our understanding of atomic properties under extreme conditions: The electric field strength seen by an electron bound to a nucleus at the distance of the Bohr radius ranges from 1010 V/cm in hydrogen to1016 V/cm in hydrogenlike uranium. The theory of quantum electrodynamics (QED) allows for calculation e.g. of binding energies, transition probabilities or magnetic moments. While at low fields QED is tested to very high precision, new, hypothetical nonlinear effects like photon- photon interaction or a violation of Lorentz symmetry may occur in strong fields which then would lead to an extension of the Standard Model. The ultra-high p…
Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution
2015
We quantify a limitation in the usual accounting of the finite-size effects, where the leading $[(Z\alpha)^4]$ and subleading $[(Z\alpha)^5]$ contributions to the Lamb shift are given by the mean-square radius and the third Zemach moment of the charge distribution. In the presence of any non-smooth behaviour of the nuclear form factor at scales comparable to the inverse Bohr radius, the expansion of the Lamb shift in the moments breaks down. This is relevant for some of the explanations of the "proton size puzzle". We find, for instance, that the de R\'ujula toy model of the proton form factor does not resolve the puzzle as claimed, despite the large value of the third Zemach moment. Withou…
THE ARITHMETIC BOHR RADIUS
2007
We study the arithmetic Bohr radius of Reinhardt domains in ℂ n which was successfully used in our study of monomial expansions for holomorphic functions in infinite dimensions. We show that this new Bohr radius is different from the radii invented by Boas and Khavinson and Aizenberg. It gives an explicit formula for the n-dimensional hypercone (which means n-dimensional variants of classical results of Bohr and Bombieri), and moreover asymptotically corrects upper and lower estimates for various types of convex and non-convex Reinhardt domains.