Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.

Ann Verdoodt

Revista Matemática de la Universidad Complutense de Madrid (1996)

  • Volume: 9, Issue: 2, page 295-307
  • ISSN: 1139-1138

Abstract

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Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --> K) (resp. C1(Vq --> K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --> K) and C1(Vq --> K).

How to cite

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Verdoodt, Ann. "Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.." Revista Matemática de la Universidad Complutense de Madrid 9.2 (1996): 295-307. <http://eudml.org/doc/44227>.

@article{Verdoodt1996,
abstract = {Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set \{aqn | n = 0,1,2,...\} where a and q are two units of Zp, q not a root of unity. C(Vq --&gt; K) (resp. C1(Vq --&gt; K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --&gt; K) and C1(Vq --&gt; K).},
author = {Verdoodt, Ann},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Bases ortonormales; Algebra de Banach no arquimediana; Enteros p-ádicos; Espacios de funciones diferenciables; Análisis funcional; Funciones continuas; -adic numbers; -function; non-Archimedean valued complete field; Mahler and van der Put bases; orthogonal bases},
language = {eng},
number = {2},
pages = {295-307},
title = {Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.},
url = {http://eudml.org/doc/44227},
volume = {9},
year = {1996},
}

TY - JOUR
AU - Verdoodt, Ann
TI - Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1996
VL - 9
IS - 2
SP - 295
EP - 307
AB - Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --&gt; K) (resp. C1(Vq --&gt; K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --&gt; K) and C1(Vq --&gt; K).
LA - eng
KW - Bases ortonormales; Algebra de Banach no arquimediana; Enteros p-ádicos; Espacios de funciones diferenciables; Análisis funcional; Funciones continuas; -adic numbers; -function; non-Archimedean valued complete field; Mahler and van der Put bases; orthogonal bases
UR - http://eudml.org/doc/44227
ER -

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