We introduce a class of Möbius invariant spaces of analytic functions in the unit disk, characterize these spaces in terms of Carleson type measures, and obtain a necessary and sufficient condition for a lacunary series to be in such a space. Special cases of this class include the Bloch space, the diagonal Besov spaces, BMOA, and the so-called Qp spaces that have attracted much attention lately.

Suppose that ϕ(z) is an analytic self-map of the unit disk ∆. We consider the boundedness of the composition operator C ϕ from Bloch space Ꮾ into the spaces Q T (Q T ,0) defined by a nonnegative, nondecreasing function T (r) on 0 ≤ r < ∞. 1. Introduction. Let ∆ = {z : |z| < 1} be the unit disk of complex plane C and let H(∆) be the space of all analytic functions in ∆. For a ∈ ∆, Green's functi...

Peter Schauß1,∗, Marc Cheneau, Manuel Endres, Takeshi Fukuhara, Sebastian Hild, Ahmed Omran, Thomas Pohl, Christian Gross, Stefan Kuhr, and Immanuel Bloch Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany University of Strathclyde, Department of Physics, SUPA, Glasgow G4 0NG, UK and Ludwig-Maximilians-Universit...

Central to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. While the theory of static effective property calculations goes back about 60 years, progress in the actual calculation of dynamic effective properties for periodic composites has been made only very recently. Here we discuss th...

We give a criterion for q-valent analytic functions in the unit disk to belong to Q K , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nonde-creasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Q p spaces are obtained. 1. Introduction....

Part 3. Geometric Construction of Loop Eisenstein Series 31 11. Bloch’s Map 31 12. Adeleic Loop groups and G-bundles on a Punctured Surface 33 13. Affine flag varieties and extensions of G-bundles 38 14. Relative Chern classes and Central extensions 41 15. Loop Eisenstein Series and Geometric Generating Functions 47 16. Ribbons and a Formal Analogue 48 17. Example: Loop Eisenstein Series on P1. 53

In this paper we prove an identity between the elliptic regulators of some 2-isogenous elliptic curves. This allow us to prove a new exotic relation for the elliptic curve 20A of Cremona’s tables. Also we prove the (conjectured) exotic relation for the curve 20B given by Bloch and Grayson in [3].

The functionality of current neuroimaging using the MRI machine needs to be improved to diagnose more complex problems. A new mathematical concept based on the solutions of the Bloch NMR for MRI applications was adopted to resolve functionality problemsby the inclusion of molecular interactions. The signal loss factor 'E' caused by fluctuating velocity due to compartmental boundaries in the mac...

The quantization of the electronic two site system interacting with a vibration is considered by using as the integrable reference system the decoupled oscillators resulting from the adiabatic approximation. A specific Bloch projection method is applied which demonstrates how besides some regular regions in the fine structure of the spectrum and the associated eigenvectors irregularities appear...

Let φ be a holomorphic self-map of a bounded homogeneous domain D in C. In this work, we show that the composition operator Cφ : f 7→ f ◦ φ is bounded on the Bloch space B of the domain and provide estimates on its operator norm. We also give a sufficient condition for φ to induce an isometry on B. This condition allows us to construct non-trivial examples of isometric composition operators in ...