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Division Problem of a Regular Form: The Case ð ‘¥ ð Ÿ ð ‘¢ = 𠜆 ð ‘¥ ð ‘£

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  • M. Mejri

Abstract

We present a systematic study of a regular linear functional 𠑣 to find all regular forms 𠑢 which satisfy the equation 𠑥 2 𠑢 = 𠜆 𠑥 𠑣 , 𠜆 ∈ ℂ − { 0 } . We also give the second-order recurrence relation of the orthogonal polynomial sequence with respect to 𠑢 and study the semiclassical character of the found families. We conclude by treating some examples.

Suggested Citation

  • M. Mejri, 2011. "Division Problem of a Regular Form: The Case ð ‘¥ ð Ÿ ð ‘¢ = 𠜆 ð ‘¥ ð ‘£," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-23, May.
    • Handle: RePEc:hin:jijmms:794593
    DOI: 10.1155/2011/794593
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