The Remez inequality for linear combinations of shifted Gaussians Academic Article uri icon

abstract

  • Let |f|:= supt|f(t)| and Gn:= f: f(t) = j=1n aje-(t-j)2, aj, j }. We prove that there is an absolute constant c1 > 0 such that [ exp (c1 (min{n{1/2}s, ns2} + s 2) f exp (80(min{n{1/2}s, ns2} + s2) for every s (0, ) and n 9, where the supremum is taken for all f Gn with m ({t }|f(t)| 1}) 7le; s. This is what we call (an essentially sharp) Remez-type inequality for the class Gn. We also prove the right higher dimensional analog of the above result. Cambridge Philosophical Society 2008.

published proceedings

  • MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

author list (cited authors)

  • Erdelyi, T.

citation count

  • 5

complete list of authors

  • Erdelyi, Tamas

publication date

  • May 2009