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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Spectral analysis for the generalized Hermite polynomials
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by Allan M. Krall PDF
Trans. Amer. Math. Soc. 344 (1994), 155-172 Request permission

Abstract:

The operator theory associated with the Hermite polynomials does not extend to the generalized Hermite polynomials because the even and odd polynomials satisfy different differential equations. We show that this leads to two problems, each of interest on its own. We then weld them together to form a united spectral expansion. In addition, the exponent $\mu$ in the weight $|x{|^{2\mu }}{e^{ - {x^2}}}$ has traditionally always been greater than $- \frac {1}{2}$. We show what happens if $\mu \leq - \frac {1}{2}$. Finally, we examine the differential equations in left-definite spaces.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 155-172
  • MSC: Primary 33C45; Secondary 34B30, 34L10, 47B50, 47E05
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1242783-9
  • MathSciNet review: 1242783