The Classical Moment Problem as a Self-Adjoint Finite Difference Operator

Advances in Mathematics

Volumn 137, Issue 1, 1998, Pages 82-203

  Simon, Barry ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002672593     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1728     Document Type: Article

References (39)

1. Akhiezer N. I. The Classical Moment Problem. 1965;Hafner, New York.
2. Akhiezer N. I., Glazman I. M. Theory of Linear Operators in Hilbert Space. 1961;Ungar, New York.
3. Alonso A., Simon B. The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators. J. Operator Theory. 4:1980;251-270.
4. Baker G., Graves-Morris P. Padé Approximants. 1996;Cambridge Univ. Press, New York.
5. Dunford N., Schwartz J. Linear Operators, II. Spectral Theory. 1963;Interscience, New York.
6. F. Gesztesy, B. Simon, J. Anal. Math.
7. de Lamadrid J. Gil. Determinacy theory for the Livšic moments problem. J. Math. Anal. Appl. 34:1971;429-444.
8. Hamburger H. Über eine Erweiterung des Stieltjesschen Momentproblems. Math. Ann. 81:1920;235-319.
9. Ismail M. E. H., Masson D. qq. Trans. Amer. Math. Soc. 346:1994;63-116.
10. M. E. H. Ismail, M. Rahman, Theq, J. Math. Anal. Appl.
11. S. Jitomirskaya, Y. Last, Power law subordinacy and singular spectra, I. Half-line operators.
12. Kato T. Perturbation Theory of Linear Operators. 1980;Springer-Verlag, New York.
13. Katznelson Y. An Introduction to Harmonic Analysis. 1976;Dover, New York.
14. U. Keich, 1997.
15. Krein M. G. Chebyshev's and Markov's ideas in the theory of limiting values of integrals and their further development. Uspekhi Matem. Nauk. 44:1951.
16. Krein M. G. On a generalization of an investigation by Stieltjes. Dokl. Akad. Nauk SSSR. 87:1952.
17. Krein M. G. Some new problems in the theory of oscillations of Sturm systems. Prikl. Mat. Mekh. 16:1952;555-568.
18. Krein M. G. On an extrapolation problem due to Kolmogorov. Dokl. Akad. Nauk. SSSR. 46:1945;306-309.
19. Landau H. The classical moment problem: Hilbertian proofs. J. Funct. Anal. 38:1980;255-272.
20. Langer R. W. More determinacy theory for the Livšic moments problem. J. Math. Anal. Appl. 56:1976;586-616.
21. Livšic M. S. On an application of the theory of hermitian operators to the generalized problem of moments. Dokl. Akad. Nauk. SSSR. 26:1940;17-22.
22. Loeffel J. J., Martin A., Simon B., Wightman A. S. Padé approximants and the anharmonic oscillator. Phys. Lett. B. 30:1969;656-658.
23. ∞. J. Funct. Anal. 10:1972;19-32.
24. Naimark M. A. Self-adjoint extensions of the second kind of a symmetric operator. Izv. Akad. Nauk SSSR. 4:1940;90-104.
25. Naimark M. A. Spectral functions of a symmetric operator. Izv. Akad. Nauk SSSR. 4:1940;309-318.
26. Naimark M. A. On spectral functions of a symmetric operator. Izv. Akad. Nauk SSSR. 7:1943;285-296.
27. Naimark M. A. On extremal spectral functions of a symmetric operator. Dokl. Akad. Nauk SSSR. 54:1946;7-9.
28. Nelson E. Analytic vectors. Ann. of Math. 70:1959;572-615.
29. Nevanlinna R. Asymptotische Entwickelungen beschränkter Functionen und das Stieltjessche Momentenproblem. Ann. Acad. Sci. Fenn. A. 18:1922.
30. Nussbaum A. Quasi-analytic vectors. Ark. Mat. 6:1965;179-191.
31. Nussbaum A. A note on quasi-analytic vectors. Studia Math. 33:1969;305-310.
32. Pearson D. B. Quantum Scattering and Spectral Theory. 1988;Academic Press, London.
33. Reed M., Simon B. Methods of Modern Mathematical Physics, I. Functional Analysis. 1972;Academic Press, New York.
34. Reed M., Simon B. Methods of Modern Mathematical Physics, II. Fourier Analysis, Self-Adjointness. 1975;Academic Press, New York.
35. Shohat J. A., Tamarkin J. D. The problem of moments. Amer. Math. Soc. Surveys. 1:1943.
36. Simon B. Coupling constant analyticity for the anharmonic oscillator. Ann. Phys. 58:1970;76-136.
37. Simon B. A canonical decomposition for quadratic forms with applications to monotone convergence theorems. J. Funct. Anal. 28:1978;377-385.
38. Stieltjes T. Recherches sur les fractions continues. Anns. Fac. Sci. Univ. Toulouse. 8:1894-1895;J1-J122.
39. Stone M. H. Linear Transformations in Hilbert Space. Amer. Math. Soc. Colloq. 1932;Publ. XV, New York.