대한수학회지 (Journal of the Korean Mathematical Society)

  • 제41권6호
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  • Pages.1049-1070
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  • 2004
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
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ORTHOGONAL POLYNOMIALS SATISFYING PARTIAL DIFFERENTIAL EQUATIONS BELONGING TO THE BASIC CLASS

  • Lee, J.K. (Department of Mathematics SunMoon University) ;
  • L.L. Littlejohn (Department of Mathematics and Statistics Utah State University) ;
  • Yoo, B.H. (Department of Mathematics Education Andong University)
  • 발행 : 2004.11.01
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초록

We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ ＋ 2B($\chi$, y) $u_{{\chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($\chi$) $u_{{\chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.

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참고문헌

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피인용 문헌

  1. Tridiagonal Operators and Zeros of Polynomials in Two Variables vol.2016, 2016, https://doi.org/10.1155/2016/6301413
  2. Bivariate orthogonal polynomials in the Lyskova class vol.233, pp.3, 2009, https://doi.org/10.1016/j.cam.2009.02.027
  3. Sobolev orthogonal polynomials in two variables and second order partial differential equations vol.322, pp.2, 2006, https://doi.org/10.1016/j.jmaa.2005.09.062
  4. On differential properties for bivariate orthogonal polynomials vol.45, pp.1-4, 2007, https://doi.org/10.1007/s11075-007-9113-3