Diophantine approximation in Banach spaces

Lior Fishman; David Simmons; Mariusz Urbanski

doi:10.5802/jtnb.871

Diophantine approximation in Banach spaces

Lior Fishman
, David Simmons
, Mariusz Urbanski

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	363-384
Number of pages	22
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	26
Issue number	2
DOIs	https://doi.org/10.5802/jtnb.871
State	Published - 1 Jan 2014
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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title = "Diophantine approximation in Banach spaces",

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.",

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AU - Simmons, David

AU - Urbanski, Mariusz

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N2 - 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.

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.

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DO - 10.5802/jtnb.871

M3 - Article

AN - SCOPUS:84924281284

SN - 1246-7405

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JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

IS - 2

ER -

Diophantine approximation in Banach spaces

Abstract

ASJC Scopus subject areas

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