We prove that if (φn) ∞ n=0, φ0 ≡ 1, is a basis in the space of entire functions of d complex variables, d ≥ 1, then for every compact K ⊂ C there is a compact K1 ⊃ K such that for every entire function f = ∑∞ n=0 fnφn we have ∑∞ n=0 |fn| supK |φn| ≤ supK1 |f |. A similar assertion holds for bases in the space of global analytic functions on a Stein manifold with the Liouville Property.

The negative energy of the hydrogen atom ensuing from Bohr's theory has been widely accepted for over a century. However, the present author considered it strange and came to the conclusion about ten years ago that it is in fact positive and is the electromagnetic energy of a condenser with unit charges of opposite sign at a distance of Bohr radius. This resulted in the finding that the latter ...

It is folklore that Albert Einstein’s greatest blunder occurred in 1917 when he introduced the cosmological constant term into his theory of general relativity [5]. At the time Einstein believed the universe to be static, and yet his original field equations, which describe how the gravitational influence of matter bends space-time, predicted an expanding (or contracting) one. To resolve this a...

The Mathematical Theory of Relativity. By A. S. Eddington. Cambridge, University Press, 1923. VI + 247 pp. The Meaning of Relativity. By Albert Einstein. Translated into English by E. P. Adams. Princeton University Press, 1923. 123 pp. The Theory of General Relativity and Gravitation. By L. Silberstein. New York, Van Nostrand, 1922. IV + 141 pp. In attempting a combined review of these three bo...

We prove that for any real θ there are infinitely many values of s = σ + it with σ → 1+ and t→ +∞ such that Re {exp(iθ) logL(s, χ)} ≥ log log log log t log log log log t +O(1). The proof relies on an effective version of Kronecker’s approximation theorem. 1. Extremal values Extremal values of the Riemann zeta-function in the half-plane of absolute convergence were first studied by H. Bohr and L...

Stephan Smolka,1,* Johan R. Ott,1 Alexander Huck,2 Ulrik L. Andersen,2 and Peter Lodahl3,† 1DTU Fotonik, Department of Photonics Engineering, Technical University of Denmark, Building 345V, 2800 Kgs. Lyngby, Denmark 2DTU Physics, Department of Physics, Technical University of Denmark, Building 309, 2800 Kgs. Lyngby, Denmark 3Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Dk-210...

Quantum theory has provoked intense discussions about its interpretation since its pioneer days, beginning with Bohr’s view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein’s ontically oriented position.

Almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr’s fundamental theorem for almost periodic functions which we then generalize to almost periodic functions on general topological groups.