Exponential instability in the fractional Calder\'on problem

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on problem and the truncated Hilbert transform.Comment: 17 page

Comparing regional organizations in global multilateral institutions:ASEAN, the EU and the UN

Structural change brought about by the end of the Cold War and accelerated globalisation have transformed the global environment. A global governance complex is emerging, characterised by an ever-greater functional and regulatory role for multilateral organisations such as the United Nations (UN) and its associated agencies. The evolving global governance framework has created opportunities for regional organisations to participate as actors within the UN (and other multilateral institutions). This article compares the European Union (EU) and Association of Southeast Asian Nations (ASEAN) as actors within the UN network. It begins by extrapolating framework conditions for the emergence of EU and ASEAN actorness from the literature. The core argument of this article is that EU and ASEAN actorness is evolving in two succinct stages: Changes in the global environment create opportunities for the participation of regional organisations in global governance institutions, exposing representation and cohesion problems at the regional level. In response, ASEAN and the EU have initiated processes of institutional adaptation