Diophantine approximation in Banach spaces
Lior Fishman[1]; David Simmons[2]; Mariusz Urbański[1]
- [1] University of North Texas Department of Mathematics 1155 Union Circle #311430 Denton, TX 76203-5017, USA
- [2] Ohio State University Department of Mathematics 231 W. 18th Avenue Columbus Ohio, OH 43210-1174, USA
Journal de Théorie des Nombres de Bordeaux (2014)
- Volume: 26, Issue: 2, page 363-384
- ISSN: 1246-7405
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topFishman, Lior, Simmons, David, and Urbański, Mariusz. "Diophantine approximation in Banach spaces." Journal de Théorie des Nombres de Bordeaux 26.2 (2014): 363-384. <http://eudml.org/doc/275786>.
@article{Fishman2014,
abstract = {In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.},
affiliation = {University of North Texas Department of Mathematics 1155 Union Circle #311430 Denton, TX 76203-5017, USA; Ohio State University Department of Mathematics 231 W. 18th Avenue Columbus Ohio, OH 43210-1174, USA; University of North Texas Department of Mathematics 1155 Union Circle #311430 Denton, TX 76203-5017, USA},
author = {Fishman, Lior, Simmons, David, Urbański, Mariusz},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {10},
number = {2},
pages = {363-384},
publisher = {Société Arithmétique de Bordeaux},
title = {Diophantine approximation in Banach spaces},
url = {http://eudml.org/doc/275786},
volume = {26},
year = {2014},
}
TY - JOUR
AU - Fishman, Lior
AU - Simmons, David
AU - Urbański, Mariusz
TI - Diophantine approximation in Banach spaces
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2014/10//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 2
SP - 363
EP - 384
AB - In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.
LA - eng
UR - http://eudml.org/doc/275786
ER -
References
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