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Original Articles

Complex versus real orthogonal polynomials of two variables

References

  • Dunkl, CF, Xu Y. Orthogonal polynomials of several variables. 2nd ed. Cambridge, UK: Cambridge University Press; 2001.
  • Suetin PK. Orthogonal polynomials in two variables. Translated from the 1988 Russian original by Pankratiev EV. Amsterdam: Gordon and Breach; 1999.
  • Itô K. Complex multiple Wiener integral. Japan J Math. 1952;22:63–86.
  • Zernike F. Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode. Physica. 1934;1:689–704. doi: 10.1016/S0031-8914(34)80259-5
  • Brinkman F, Zernike HC. Hypersphärishe Funktionen und die in sphärischen Bereichen orthogonalen Polynome. Proc Kon Akad v Wet, Amsterdam. 1935;38:161–170.
  • Gazeau N, Górska JP, Cotfas K. Complex and real Hermite polynomials and related quantizations. J Phys A. 2010;43: 305304 (14 pp).
  • Ghanmi A. A class of generalized complex Hermite polynomials. J Math Anal Appl. 2008;340:1395–1406. doi: 10.1016/j.jmaa.2007.10.001
  • Ghanmi A. Operational formulae for the complex Hermite polynomials . Integral Transforms Spec Funct. 2013. doi:10.1080/10652469.2013.772172
  • Intissar A, Intissar A. Spectral properties of the Cauchy transform on . J Math Anal Appl. 2006;313:400–418. doi: 10.1016/j.jmaa.2005.09.056
  • Ismail M. Analytic properties of complex Hermite polynomials. Trans Amer Math Soc (to appear).
  • Ismail M, Simeonov P. Complex Hermite polynomials: their combinatorics and integral operators. Proc Amer Math Soc (to appear).
  • Thirulogasanthar K, Saad N, Honnouvo G. 2D-Zernike polynomials and coherent state quantization of the unit disc, arXiv:1303.5483; 2013.
  • Wünsche A. Generalized Zernike or disc polynomials. J Comput Appl Math. 2005;174:135–163. doi: 10.1016/j.cam.2004.04.004
  • Thangavelu S. Lectures on Hermite and Laguerre expansions. Princeton, NJ: Princeton University Press; 1993.
  • G Szegö. Orthogonal polynomials. 4th ed. American Mathematical Society Colloquium Publication 23. Providence, RI: American Mathematical Society; 1975.
  • Koornwinder T. Orthogonal polynomials in two varaibles which are eigenfunctions of two algebraically independent partial differential operators. Nederl Acad Wetensch Proc. Ser. A77 = Indag Math. 1974;36:357–381. doi: 10.1016/1385-7258(74)90026-2
  • Li H, Sun, J, Xu Y. Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle. SIAM J Numer Anal. 2008;46:1653–1681. doi: 10.1137/060671851

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