arXiv:1109.3429v1 [math.FA] 15 Sep 2011 Bicomplex Riesz-Fisher Theorem K. S. Charak 1 , R. Kumar 2 , D. Rochon 3 1 Department of Mathematics, University of Jammu, Jammu-180 006, INDIA. E-mail: kscharak7@rediffmail.com 2 Department of Mathematics, University of Jammu, Jammu-180 006, INDIA. E-mail: ravinder.kumarji@gmail.com 3 D´ epartement de math´ ematiques et d’informatique, Universit´ e du Qu´ ebec ` a Trois-Rivi` eres, C.P. 500, Trois-Rivi` eres, Qu´ ebec, Canada G9A 5H7. E-mail: Dominic.Rochon@UQTR.CA, Web: www.3dfractals.com Abstract This paper continues the study of infinite dimensional bicomplex Hilbert spaces introduced in [2]. Besides obtaining a Best Approximation Theo- rem, the main purpose of this paper is to obtain a bicomplex analogue of the Riesz-Fisher Theorem. Keywords: Bicomplex Numbers, Bicomplex Algebras, Hilbert spaces, Schauder basis, Orthonormal basis, Riesz-Fisher Theorem AMS [2010]: Primary 16D10; Secondary 30G35, 46C05, 46C50. 1