Infinite-Dimensional Bicomplex Hilbert Spaces

Details Infinite-Dimensional Bicomplex Hilbert Spaces Infinite-Dimensional Bicomplex Hilbert Spaces

2010-06-25

arxiv.org/abs/1006.5017v4

Ann. Funct. Anal.: Volume 1, Issue 2 (2010), Page 75-91

Mathematics

Functional Analysis

Scientific paper

This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex Hilbert space. Properties of such spaces are obtained through properties of several of their subsets which have the structure of genuine Hilbert spaces. In particular, we derive the Riesz representation theorem for bicomplex continuous linear functionals and a general version of the bicomplex Schwarz inequality. Applications to concepts relevant to quantum mechanics, specifically the bicomplex analogue of the quantum harmonic oscillator, are pointed out.

Affiliated with

Also associated with

No associations

Rating

Infinite-Dimensional Bicomplex Hilbert Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Infinite-Dimensional Bicomplex Hilbert Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite-Dimensional Bicomplex Hilbert Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-310437