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A direct proof of the functional Santalo inequality
the functional Santalo inequality math
2010/11/15
We give a simple proof of a functional version of the Blaschke-Santalo inequality due to Artstein, Klartag and Milman. The proof is by induction on the dimension and does not use the Blaschke-Santalo ...
Deciding the dimension of effective dimension reduction space for functional and high-dimensional data
effective dimension reduction space high-dimensional data
2010/11/18
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The ...
Functional self-similarity and renormalization group symmetry in mathematical physics
Functional self-similarity renormalization group symmetry mathematical physics
2010/11/1
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are...
Graph-Laplacians and Dirac Operators on (Infinite) Graphs and the Calculation of the Connes-Distance-Functional
Graph-Laplacians Dirac Operators Calculation the Connes-Distance-Functional
2010/11/1
We develop a graph-Hilbert-space framework, inspired by non-commutative geometry, on (infinite) graphs and use it to study spectral properies of \tit{graph-Laplacians} and so-called \tit{graph-Dirac-o...