Fourier Analysis Jan Wiegerinck version December 3 , 2014

Fourier Analysis Jan

2 Armen Edigarian and Jan Wiegerinck

Let D1 ⊂ D2 be domains in C. Under very mild conditions on D2 we show that there exist holomorphic functions f , defined on D1 with the property that f is nowhere extendible across ∂D1, while the graph of f over D1 is not complete pluripolar in D2 × C. This refutes a conjecture of Levenberg, Martin and Poletsky [6].

More Approximation on Disks

In this paper we study the function algebra generated by z and g on a small closed disk centered at the origin of the complex plane. We prove, using a biholomorphic change of coordinates and already developed techniques in this area, that for a large class of functions g this algebra consists of all continuous functions on the disk.

Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis

Article history: Received 4 June 2013 Received in revised form 11 November 2013 Accepted 8 December 2013 Available online 18 December 2013

EM Algorithms for Self-Organizing Maps

Self-organizing maps are popular algorithms for unsupervised learning and data visualization. Exploiting the link between vector quantization and mixture modeling, we derive EM algorithms for self-organizing maps with and without missing values. We compare self-organizing maps with the elastic-net approach and explain why the former is better suited for the visualization of high-dimensional dat...