The Digit Principle

By Keith Conrad. 2000

61 citations recorded by the source corpus.

Abstract A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We illustrate several examples of orthonormal bases from this viewpoint, and we also obtain a concrete model for the continuous functions on the integers of a local field as a quotient of a Tate algebra in countably many variables.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/d0c08c86d51c81249ddfaea415c56cb3b662bcc5

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In Computational Theory and Mathematics

1. A. M. Uludağ
2. R. Holzapfel
3. Masaaki Yoshida

In Mathematical Physics

1. A. M. Uludağ
2. R. Holzapfel
3. Masaaki Yoshida

Citations in the corpus

• Arithmetic and Geometry Around Hypergeometric Functions (2007, background): “The sequence {Dk} is an orthonormal basis of the space of continuous Fq-linear functions on O [16, 9].”