Hermitian moment sequences
HTML articles powered by AMS MathViewer
- by J. S. MacNerney PDF
- Trans. Amer. Math. Soc. 103 (1962), 45-81 Request permission
References
- R. P. Boas Jr., The Stieltjes moment problem for functions of bounded variation, Bull. Amer. Math. Soc. 45 (1939), no. 6, 399–404. MR 1563993, DOI 10.1090/S0002-9904-1939-06992-9
- R. R. Christian, On order-preserving integration, Trans. Amer. Math. Soc. 86 (1957), 463–488. MR 98165, DOI 10.1090/S0002-9947-1957-0098165-6
- Hans Hamburger, Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 81 (1920), no. 2-4, 235–319 (German). MR 1511966, DOI 10.1007/BF01564869
- Felix Hausdorff, Der Wertvorrat einer Bilinearform, Math. Z. 3 (1919), no. 1, 314–316 (German). MR 1544350, DOI 10.1007/BF01292610
- Felix Hausdorff, Momentprobleme für ein endliches Intervall, Math. Z. 16 (1923), no. 1, 220–248 (German). MR 1544592, DOI 10.1007/BF01175684
- A. Jakimovski, Some remarks on the moment problem of Hausdorff, J. London Math. Soc. 33 (1958), 1–14. MR 92020, DOI 10.1112/jlms/s1-33.1.1
- M. Kreĭn, Infinite $J$-matrices and a matrix-moment problem, Doklady Akad. Nauk SSSR (N.S.) 69 (1949), 125–128 (Russian). MR 0034964
- J. S. MacNerney, Half-bounded matrices, J. Indian Math. Soc. (N.S.) 16 (1952), 151–176 (1953). MR 52481
- J. S. MacNerney, Investigation concerning positive definite continued fractions, Duke Math. J. 26 (1959), 663–677. MR 117326, DOI 10.1215/S0012-7094-59-02664-X
- J. S. MacNerney, Hellinger integrals in inner product spaces, J. Elisha Mitchell Sci. Soc. 76 (1960), 251–273. MR 126708
- Edward J. McShane, Order-preserving maps and integration processes, Annals of Mathematics Studies, No. 31, Princeton University Press, Princeton, N. J., 1953. MR 0056064 F. Riesz, Sur les opérations fonctionnelles linéaire, C. R. Acad. Sci. Paris 149 (1909), 974-977. —, Les systèmes d’équations linéaires à une infinité d’inconnues, Gauthier-Villars, Paris, 1913. —, Zur Theorie des Hilbertschen Raumes, Acta Sci. Math. Szeged 7 (1934), 34-38. F. Riesz and B. Sz.-Nagy, Leçons d’analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1952. —, Functional analysis, Ungar, New York, 1955. (translation of second French edition of [15])
- T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse Math. (6) 4 (1995), no. 1, Ji–Jiv, J1–J35 (French). Reprint of the 1894 original; With an introduction by Jean Cassinet. MR 1344720, DOI 10.5802/afst.789
- Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877, DOI 10.1090/coll/015
- John von Neumann, Functional Operators. II. The Geometry of Orthogonal Spaces, Annals of Mathematics Studies, No. 22, Princeton University Press, Princeton, N. J., 1950. MR 0034514
- H. S. Wall, Continued fractions and totally monotone sequences, Trans. Amer. Math. Soc. 48 (1940), 165–184. MR 2642, DOI 10.1090/S0002-9947-1940-0002642-0
- H. S. Wall, Bounded $J$-fractions, Bull. Amer. Math. Soc. 52 (1946), 686–693. MR 17397, DOI 10.1090/S0002-9904-1946-08630-9
- H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Co., Inc., New York, N. Y., 1948. MR 0025596 —, J-matrices of interior order k, Abstract 137t, Bull. Amer. Math. Soc. 57 (1951), 134.
- J. H. Wells, Concerning the Hausdorff inclusion problem, Duke Math. J. 26 (1959), 629–645. MR 109969, DOI 10.1215/S0012-7094-59-02661-4
Additional Information
- © Copyright 1962 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 103 (1962), 45-81
- MSC: Primary 44.60
- DOI: https://doi.org/10.1090/S0002-9947-1962-0150550-1
- MathSciNet review: 0150550