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<p>The paper describes solutions of the Laplace–Beltrami equation on a two-dimensional two-sheeted hyperboloid for three non-subgroup coordinate systems: semi-circular parabolic, elliptic parabolic and hyperbolic parabolic. The coefficients of interbasis expansions of solutions in these coordinates through some subgroup bases are calculated. A contraction procedure for all normalized eigenfunctions in the specified coordinate systems from the hyperboloid to the Euclidean plane is realized.</p>

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Lie algebra contractions and interbasis expansions on two-dimensional hyperboloid. IIB. Non-subgroup bases

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • George S. Pogosyan,
  • Alexander Yakhno

摘要

The paper describes solutions of the Laplace–Beltrami equation on a two-dimensional two-sheeted hyperboloid for three non-subgroup coordinate systems: semi-circular parabolic, elliptic parabolic and hyperbolic parabolic. The coefficients of interbasis expansions of solutions in these coordinates through some subgroup bases are calculated. A contraction procedure for all normalized eigenfunctions in the specified coordinate systems from the hyperboloid to the Euclidean plane is realized.