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Displaying similar documents to “On values of homogeneous polynomials in discrete sets of points”

Volume ratios in L p -spaces

Yehoram Gordon, Marius Junge (1999)

Studia Mathematica

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There exists an absolute constant c 0 such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that i n f e l l i p s o i d ε B E ( v o l ( B E ) / v o l ( ε ) ) 1 / n c 0 i n f z o n o i d Z B F ( v o l ( B F ) / v o l ( Z ) ) 1 / k . The concept of volume ratio with respect to p -spaces is used to prove the following distance estimate for 2 q p < : s u p F p , d i m F = n i n f G L q , d i m G = n d ( F , G ) c p q n ( q / 2 ) ( 1 / q - 1 / p ) .

Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

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Let R ( λ ) be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that 1 T | R ( t ) | 2 d t = c T 5 2 + O δ ( T 9 4 + δ ) , where c is a specific nonzero constant and δ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that R ( t ) = O δ ( t 3 4 + δ ) .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the 2 n + 1 -dimensional case. ...