Applications of spherical designs to Banach space theory

Hermann König. "Applications of spherical designs to Banach space theory." Banach Center Publications 64.1 (2004): 127-134. <http://eudml.org/doc/282123>.

@article{HermannKönig2004,
abstract = {Spherical designs constitute sets of points distributed on spheres in a regular way. They can be used to construct finite-dimensional normed spaces which are extreme in some sense: having large projection constants, big or small Banach-Mazur distance to Hilbert spaces or $ℓ_p$-spaces. These examples provide concrete illustrations of results obtained by more powerful probabilistic techniques which, however, do not exhibit explicit examples. We give a survey of such constructions where the geometric invariants can be estimated quite precisely.},
author = {Hermann König},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {127-134},
title = {Applications of spherical designs to Banach space theory},
url = {http://eudml.org/doc/282123},
volume = {64},
year = {2004},
}

TY - JOUR
AU - Hermann König
TI - Applications of spherical designs to Banach space theory
JO - Banach Center Publications
PY - 2004
VL - 64
IS - 1
SP - 127
EP - 134
AB - Spherical designs constitute sets of points distributed on spheres in a regular way. They can be used to construct finite-dimensional normed spaces which are extreme in some sense: having large projection constants, big or small Banach-Mazur distance to Hilbert spaces or $ℓ_p$-spaces. These examples provide concrete illustrations of results obtained by more powerful probabilistic techniques which, however, do not exhibit explicit examples. We give a survey of such constructions where the geometric invariants can be estimated quite precisely.
LA - eng
UR - http://eudml.org/doc/282123
ER -