## 510 Mathematik

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In this note we look at anisotropic approximation of smooth functions on bounded domains with tensor product splines. The main idea is to extend such functions and then use known approximation techniques on Rd. We prove an error estimate for domains for which bounded extension operators exist. This obvious approach has some limitations. It is not applicable without restrictions on the chosen coordinate degree even if the domain is as simple as the unit disk. Further for approximation on Rd there are error estimates in which the grid widths and directional derivatives are paired in an interesting way. It seems impossible to maintain this property using extension operators.

In this article feedback linearization for control-affine nonlinear systems is extended to systems where linearization is not feasible in the complete state space by combining state feedback linearization and homotopy numerical continuation in subspaces of the phase space where feedback linearization fails. Starting from the conceptual simplicity of feedback linearization, this new method expands the scope of their applicability to irregular systems with poorly expressed relative degree. The method is illustrated on a simple SISO–system and by controlling the speed and the rotor flux linkage in a three phase induction machine.

This paper analyzes governance mechanisms for different group sizes. The European sovereign debt crisis has demonstrated the need of efficient governance for different group sizes. I find that self-governance only works for sufficiently homogenous and small neighbourhoods. Second, as long as the union expands, the effect of credible self-governance decreases. Third, spill-over effects amplify the size effect. Fourth, I show that sufficiently large monetary unions, are better off with costly but external governance or a free market mechanism. Finally, intermediate-size unions are most difficult to govern efficiently.

Applied mathematical theory for monetary-fiscal interaction in a supranational monetary union
(2014)

I utilize a differentiable dynamical system á la Lotka-Voletrra and explain monetary and fiscal interaction in a supranational monetary union. The paper demonstrates an applied mathematical approach that provides useful insights about the interaction mechanisms in theoretical economics in general and a monetary union in particular. I find that a common central bank is necessary but not sufficient to tackle the new interaction problems in a supranational monetary union, such as the free-riding behaviour of fiscal policies. Moreover, I show that upranational institutions, rules or laws are essential to mitigate violations of decentralized fiscal policies.