Small eigenvalues of large Hankel matrices: The indeterminate case

Mathematica Scandinavica

Volumn 91, Issue 1, 2002, Pages 67-81

  Berg, Christian ^a   Chen, Yang ^a   Ismail, Mourad E H ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036400774     PISSN: 00255521     EISSN: None     Source Type: Journal    
DOI: 10.7146/math.scand.a-14379     Document Type: Article

References (14)

1. Akhiezer, N.I., The Classical Moment Problem and Some Related Questions in Analysis, English translation, Oliver and Boyd, Edinburgh, 1965.
2. Al-Salam, W.A. and Carlitz, L., Some orthogonal q-polynomials, Math. Nachr. 30 (1965), 47-61.
3. Berg, C., and Valent, G., The Nevanlinna parametrization for some indeterminate Stieltjes moment problems associated with birth and death processes, Methods and Applications of Analysis 1 (1994), 169-209.
4. Chihara, T.S., An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
5. Chen, Y. and Ismail, M.E.H., Some indeterminate moment problems and Freud-like weights, Constr. Approx. 14 (1998), 439-458.
6. Chen, Y. and Lawrence, N.D., Small eigenvalues of large Hankel matrices, J. Phys. A 32 (1999), 7305-7315.
7. Gasper, G. and Rahman, M., Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
8. Hamburger, H., Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 81 (1920), 235-319, 82, 120-164, 168-187.
9. Ismail, M.E.H. and Masson, D.R., q-Hermite polynomials, biorthogonal rational functions, and q-beta integrals, Trans. Amer. Math. Soc. 346 (1994), 63-116.
10. Shohat, J. and Tamarkin, J.D., The Problem of Moments, Revised edition, American Mathematical Society, Providence, 1950.
11. Szego, G., On some Hermitian forms associated with two given curves of the complex plane, Collected papers (volume 2), 666-678. Birkhaüser, Boston, Basel, Stuttgart, 1982.
12. Szego, G., Orthogonal Polynomials, Fourth Edition, American Mathematical Society, Providence, 1975.
13. Widom, H. and Wilf, H.S., Small eigenvalues of large Hankel matrices, Proc. Amer. Math. Soc. 17 (1966), 338-344.
14. Wilf, H.S., Finite Sections of some Classical Inequalities, Springer, Berlin, Heidelberg, New York, 1970.