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MiS Preprint
60/2005
Best N-term approximation in electronic structure calculations.I. One-electron reduced density matrix
Heinz-Jürgen Flad, Wolfgang Hackbusch and Reinhold Schneider
Abstract
We discuss best $N$-term approximation spaces for one-electron wavefunctions $\phi_i$ and reduced density matrices $\rho$ emerging from Hartree-Fock and density functional theory. The approximation spaces $A^\alpha_q(H^1)$ for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted $\ell_q$ spaces of wavelet coefficients to proof that both $\phi_i$ and $\rho$ are in $A^\alpha_q(H^1)$ for all $\alpha > 0$ with $\alpha = \frac{1}{q} - \frac{1}{2}$. Our proof is based on the assumption that the $\phi_i$ possess an asymptotic smoothness property at the electron-nuclear cusps.
