Abstract
In a recent paper (Nasir, 2007), a set of weakly orthogonal and completely orthogonal spherical harmonics in a non-polar spherical coordinate system based on a cubed-sphere was constructed. In this work, we explore some linear relations between these two sets of spherical harmonics. Moreover, a power representation for the set of weakly orthogonal spherical harmonics corresponding to a mode is presented. We also determine the norm of the orthogonal spherical harmonics and hence the inner products for the weakly orthogonal spherical harmonics. As an immediate application of these properties, we present a Fourier series formulation of spherical functions defined on the cubed-sphere.
Keywords
Subject
Publication details
- DOI
- 10.24200/squjs.vol17iss2pp200-213
- Journal
- Sultan Qaboos University Journal for Science, 17(2), 200
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Faham, M. A. A. M., & Nasir, H. M. (2012). Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere. Sultan Qaboos University Journal for Science, 17(2), 200. https://doi.org/10.24200/squjs.vol17iss2pp200-213
MLA 9
Faham, M. A. A. M., and Haniffa Mohamed Nasir. "Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere." Sultan Qaboos University Journal for Science, vol. 17, no. 2, 2012, pp. 200. https://doi.org/10.24200/squjs.vol17iss2pp200-213.
Chicago (author–date)
Faham, M. A. A. M., and Haniffa Mohamed Nasir. 2012. "Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere." Sultan Qaboos University Journal for Science 17 (2): 200. https://doi.org/10.24200/squjs.vol17iss2pp200-213.
Harvard
Faham, M. A. A. M. and Nasir, H. M. (2012) 'Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere', Sultan Qaboos University Journal for Science, 17(2), pp. 200. doi:10.24200/squjs.vol17iss2pp200-213.
Vancouver
Faham MAAM, Nasir HM. Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere. Sultan Qaboos University Journal for Science. 2012;17(2):200. doi:10.24200/squjs.vol17iss2pp200-213
IEEE
M. A. A. M. Faham, and H. M. Nasir, "Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere," Sultan Qaboos University Journal for Science, vol. 17, no. 2, pp. 200, 2012, doi: 10.24200/squjs.vol17iss2pp200-213.