Solutions of the strong Hamburger moment problem

Journal of Mathematical Analysis and Applications

Volumn 197, Issue 1, 1996, Pages 227-248

  Njåstad, Olav ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0029704177     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0017     Document Type: Article

References (35)

1. 1. N. I. Akhiezer, "The Classical Moment Problem and Some Related Questions in Analysis," Hafner, New York, 1965.
2. 2. C. Berg, J. P. R. Christensen, and P. Ressel, "Harmonic Analysis on Semigroups," Springer-Verlag, Berlin, 1984.
3. 3. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njåstad, The computation of orthogonal rational functions and their interpolating properties, Numer. Algorithms 2 (1992), 85-114.
4. 4. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njåstad, Moment problems and orthogonal functions. J. Comput. Appl. Math. 48 (1993), 217-228.
5. 5. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njåstad, Orthogonal rational functions with poles on the unit circle, J. Math. Anal. Appl. 182 (1994), 221-243.
6. 6. T. S. Chihara, "An Introduction to Orthogonal Polynomials," Mathematics and Its Applications Series, Gordon and Breach, New York, 1978.
7. 7. L. Cochran and S. Clement Cooper, Orthogonal Laurent polynomials on the real line, in "Continued Fractions and Orthogonal Functions" (S. Clement Cooper and W. J. Thron, Eds.), 47-101, Dekker, New York, 1994.
8. 8. M. M. Djrbashian, A survey on the theory of orthogonal systems and some open problems, in "Orthogonal Polynomials: Theory and Practice" (P. Nevai, Ed.), pp. 135-146, Kluwer, Dordrecht/Boston/London, 1990.
9. 9. H. Hamburger, Über eine Erweiterung des Stieltjesschen Momenten problems, I, II, III, Math. Annalen 81 (1920), 235-319; 82 (1921), 120-164, 168-187.
10. 9. H. Hamburger, Über eine Erweiterung des Stieltjesschen Momenten problems, I, II, III, Math. Annalen 81 (1920), 235-319; 82 (1921), 120-164, 168-187.
11. 10. E. Hendriksen and H. van Rossum, Orthogonal Laurent polynomials, Indag. Math. 89 (1986), 17-36.
12. 11. W. B. Jones, O. Njåstad, and W. J. Thron, Orthogonal Laurent polynomials and the strong Hamburger moment problem, J. Math. Anal. Appl. 98 (1984), 528-554.
13. 12. W. B. Jones, O. Njåstad, and W. J. Thron, Continued fractions and strong Hamburger moment problems, Proc. Lond. Math. Soc. (3) 47 (1983), 363-384.
14. 13. W. B. Jones, O. Njåstad, and W. J. Thron, Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle, Bull. London Math. Soc. 21 (1989), 133-152.
15. 14. W. B. Jones and W. J. Thron, Orthogonal Laurent polynomials and Gaussian quadrature, "Quantum Mechanics in Mathematics, Chemistry, and Physics" (K. Gustafson and W. P. Reinhardt, Eds.), pp. 449-455, Plenum, New York, 1981.
16. 15. W. B. Jones and W. J. Thron, Survey of continued fractions methods of solving moment problems and related topics, in "Analytic Theory of Continued Fractions" (W. B. Jones, W. J. Thron, H. Waadeland, Eds.), Lecture Notes in Mathematics, Vol. 932, pp. 4-37, Springer-Verlag, Berlin, 1982.
17. 16. W. B. Jones and W. J. Thron, Continued fractions: Analytic theory and applications, in "Encyclopedia of Mathematics and Its Applications," Vol. 11, Addison-Wesley, Reading, MA, 1980.
18. 17. W. B. Jones, W. J. Thron and H. Waadeland, A strong Stieltjes moment problem, Trans. Amer. Math. Soc. 206 (1980), 503-528.
19. 18. H. J. Landau, The classical moment problem: Hilbertian proofs, J. Funct. Anal. 38 (1980), 255-272.
20. 19. H. J. Landau (Ed.), "Moments in Mathematics," Proceedings of Symposia in Applied Mathematics, Vol. 37, Amer. Math. Soc., Providence, RI, 1987.
21. 20. R. Nevanlinna, Über beschränkte analytische Funktionen, Ann. Acad. Sci. Fenn. A 18, No. 5, 1-52.
22. 21. O. Njåstad, An extended Hamburger moment problem, Proc. Edinburgh Math. Soc. 28 (1985), 167-183.
23. 22. O. Njåstad, Unique solvability of an extended Hamburger moment problem, J. Math. Anal. Appl. 124 (1987), 502-519.
24. 23. O. Njåstad and W. J. Thron, The theory of sequences of orthogonal L-polynomials, in "Padé Approximants and Continued Fractions" (H. Waadeland and H. Wallin, Eds.), Del. Kongelige Norske Videnskabers Selskab, Vol. 1, pp. 54-91, 1983.
25. 24. O. Njåstad and W. J. Thron, Unique solvability of the strong Hamburger moment problem, J. Austral. Math. Soc. Ser. A 40 (1986), 5-19.
26. 25. A. Sri Ranga, J-fractions and strong moment problems, in "Analytic Theory of Continued Fractions" (W. J. Thron, Ed.), Lecture Notes in Mathematics, Vol. 1199, pp. 269-284, Springer-Verlag, Berlin, 1986.
27. 26. M. Riesz, Sur le problème des moments, I, II, III, Arkiv. Matematik, Astron. Fys. 16, No. 12 (1921), 23; 16, No. 119 (1922), 21; 17, No. 16 (1923), 52.
28. 26. M. Riesz, Sur le problème des moments, I, II, III, Arkiv. Matematik, Astron. Fys. 16, No. 12 (1921), 23; 16, No. 119 (1922), 21; 17, No. 16 (1923), 52.
29. 26. M. Riesz, Sur le problème des moments, I, II, III, Arkiv. Matematik, Astron. Fys. 16, No. 12 (1921), 23; 16, No. 119 (1922), 21; 17, No. 16 (1923), 52.
30. 27. J. A. Shohat and J. D. Tamarkin, "The Problem of Moments," Mathematical Surveys, Vol. 1, Amer. Math. Soc., Providence, RI, 1943.
31. 28. T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse 8 (1894), J1-J122; 9 (1894), A1-A47; Oeuveres 2, 402-566.
32. 28. T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse 8 (1894), J1-J122; 9 (1894), A1-A47; Oeuveres 2, 402-566.
33. 28. T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse 8 (1894), J1-J122; 9 (1894), A1-A47; Oeuveres 2, 402-566.
34. 29. M. H. Stone, "Linear Transformations in Hilbert Space and Their Applications to Analysis," Amer. Math. Soc. Colloquium Publ., Vol. 15, Amer. Math. Soc., New York, 1932.
35. 30. G. Szegö, "Orthogonal Polynomials," Amer. Math. Soc. Coll. Publ. Vol. 23, 4th ed., Amer. Math. Soc., Providence, RI, 1925.