On the growth of Lebesgue constants for convex polyhedra

We prove an upper bound on the energy density of the dilute spin-1 2 Fermi gas capturing the leading correction to the kinetic energy 8πaρ ↑ ρ ↓ with an error of size smaller than aρ 2 (a 3 ρ) 1/3−ε for any ε > 0, where a denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237-260).

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The Lebesgue Constants of Fourier Partial Sums

Ganzburg

Liflyand

2019

Topics in Classical and Modern Analysis

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On the growth of Lebesgue constants for convex polyhedra

Abstract: Abstract. In the paper, new estimates of the Lebesgue constantwhere s is size of the triangulation of W .

Cited by 10 publications

References 20 publications

Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion

Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion

Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion

The Lebesgue Constants of Fourier Partial Sums

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