Ghost matrices and a characterization of symmetric Sobolev bilinear forms

Linear Algebra and Its Applications

Volumn 431, Issue 1-2, 2009, Pages 104-119

  Kwon, K H ^a   Littlejohn, Lance L ^b   Yoon, G J ^c  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b BAYLOR UNIVERSITY   (United States)

^c Korea Institute for Advanced Study   (South Korea)

Author keywords

Ghost function; Ghost matrix; Moment functional; Orthogonal polynomials; Symmetric bilinear form

Indexed keywords

GHOST FUNCTION; GHOST MATRIX; MOMENT FUNCTIONAL; ORTHOGONAL POLYNOMIALS; SYMMETRIC BILINEAR FORM;

FOURIER ANALYSIS;

POLYNOMIAL APPROXIMATION;

EID: 65049083265     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2009.02.014     Document Type: Article

References (22)

1. Álvarez de Morales M., Pérez T.E., Piñar M.A., and Ronveaux A. Orthogonal polynomials associated with a nondiagonal Sobolev inner product with polynomial coefficients. Orthogonal Functions, Moment Theory, and Continued Fractions. Theory and Applications (Campinas, 1996). Lecture Notes in Pure and Applied Mathematics vol. 199 (1998), Marcel Dekker, New York 343-358
2. G.E. Andrews, L.L. Littlejohn, A combinatorial interpretation of the Legendre-Stirling numbers, Proc. Amer. Math. Soc., in press.
3. Barrios Rolania D., López-Lagomasino G., and Pijeira Cabrera H. The moment problem for a Sobolev inner product. J. Approx. Theory 100 2 (1999) 364-380
4. J. Blankenagel, Anwendungenadjungierter Polynomoperatoren, Doctoral Dissertation, Universität Köln, 1971.
5. Boas R.P. The Stieltjes moment problem for functions of bounded variation. Bull. Amer. Math. Soc. 45 (1939) 399-404
6. Chihara T.S. An Introduction to Orthogonal Polynomials (1978), Gordon and Breach Publishers, New York
7. Danese A.E. Present status and current trends in the theory of orthogonal polynomials and special functions. Rend. Sem. Mat. Univers. Politec. Torino 35 (1976/1977) 1-20
8. Duran A.J. The Stieltjes moment problem for rapidly decreasing functions. Proc. Amer. Math. Soc. 107 (1989) 731-741
9. Duran A.J. Functions with given moments and weight functions for orthogonal polynomials. Rocky Mountain J. Math. 23 (1993) 87-104
10. Gautschi W. Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation Series (2004), Oxford University Press, London
11. Han S.S., Kim S.S., and Kwon K.H. Orthogonalizing weights for Tchebycheff sets of polynomials. Bull. London Math. Soc. 24 (1992) 361-367
12. Krall H.L., and Frink O. A new class of orthogonal polynomials: the Bessel polynomials. Trans. Amer. Math. Soc. 65 (1949) 100-115
13. Kwon K.H., and Littlejohn L.L. Sobolev orthogonal polynomials and second-order differential equations. Rocky Mountain J. Math. 28 2 (1998) 547-594
14. Lay D.C. Linear Algebra and its Applications. third edition. (2003), Addison-Wesley Publishing Co., New York
15. Littlejohn L.L. On the classification of differential equations having orthogonal polynomial solutions. Ann. Mat. Pura Appl. 4 (1984) 35-53
16. Marcellán F., Alfaro M., and Rezola M.L. Orthogonal polynomials on Sobolev spaces: old and new directions. J. Comput. Appl. Math. 49 (1993) 225-232
17. Marcellán F., and Szafraniec F.H. The Sobolev-type moment problem. Proc. Amer. Math. Soc. 128 (2000) 2309-2317
18. Marcellán F., and Szafraniec F.H. A matrix algorithm towards solving the moment problem of Sobolev type. Linear Algebra Appl. 331 1-2 (2001) 155-164
19. Piziak R., and Odell P.L. Matrix Theory: From Generalized Inverses to Jordan Form. Pure and Applied Mathematics Series (2007), Chapman and Hall/CRC, Boca Raton
20. Schäfke F.W., and Wolf G. Einfache verallgemeinerte Klassische orthogonalpolynome. J. Reine Angew. Math. 262-263 (1973) 339-355
21. Stieltjes T.J. Recherches sur les fractions continues. Ann. Faculte Sci. Toulousse 1 (1894) [T 1 122, 1 9 A 5-47]
22. Szegö G. Orthogonal Polynomials. fourth ed. vol. 23 (1975), American Mathematical Society Colloquium Publications, Providence, Rhode Island