DISCRETE SOBOLEV ORTHOGONAL POLYNOMIALS AND SECOND ORDER DIFFERENCE EQUATIONS

  • Jung, H.S. (Department of Mathematics KAIST) ;
  • Kwon, K.H. (Department of Mathematics KAIST) ;
  • Lee, D.W. (Topology and Geometry Research Center Kyungpook National University)
  • 발행 : 1999.03.01

초록

Let {Rn($\chi$)}{{{{ { } atop {n=0} }}}} be a discrete Sobolev orthogonal polynomials (DSOPS) relative to a symmetric bilinear form (p,q)={{{{ INT _{ } }}}} pqd$\mu$0 +{{{{ INT _{ } }}}} p qd$\mu$1, where d$\mu$0 and d$\mu$1 are signed Borel measures on . We find necessary and sufficient conditions for {Rn($\chi$)}{{{{ { } atop {n=0} }}}} to satisfy a second order difference equation 2($\chi$) y($\chi$)+ 1($\chi$) y($\chi$)= ny($\chi$) and classify all such {Rn($\chi$)}{{{{ { } atop {n=0} }}}}. Here, and are forward and backward difference operators defined by f($\chi$) = f($\chi$+1) - f($\chi$) and f($\chi$) = f($\chi$) - f($\chi$-1).

키워드

second order difference equations;discrete Sobolev orthogonal polynomials

참고문헌

  1. J. Comp. Appl. Math. v.57 A distributional study of diserete classical orthogonal polynomials A. G. Garcia;F. Marcellan;L. Salto
  2. Bull. Amer. Math. Soc. v.45 The Stieltjes moment problem for functions of bounded variation R. P. Boas
  3. Proc. Amer. Math. Soc. v.107 The Stieltjes moment problem for rapidly decreasing functions A. J. Duran
  4. J. Approx. Th. v.89 New characterizations of discrete classical orthogonal polynomials K. H. Kwon;D. W. Lee;S. B. Park
  5. Classical orthogonal polynomials of a discrete variable A. F. Nikiforov;S. K. Suslov;V. B. Uvarov
  6. Ann. Mat. Pura Appl. v.74 Differential equations of infinite order for orthogonal polynomials H. L. Krall;I. M. Sheffer
  7. Rocky Mt. J. Math. Sobolev orthogonal polynomials and second order differential equations K. H. Kwon;L. L. Littlejohn
  8. J. Difference Eqs. Appl. Discrete classical orthogonal polynomials K. H. Kwon;D. W. Lee;S. B. Park;B. H. Yoo