Moment problems and polynomial approximation

Christian Berg

Annales de la Faculté des sciences de Toulouse : Mathématiques (1996)

  • Volume: S5, page 9-32
  • ISSN: 0240-2963

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Berg, Christian. "Moment problems and polynomial approximation." Annales de la Faculté des sciences de Toulouse : Mathématiques S5 (1996): 9-32. <http://eudml.org/doc/73407>.

@article{Berg1996,
author = {Berg, Christian},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Nevanlinna parametrization; moment problems; polynomial approximation; Carleman's condition},
language = {eng},
pages = {9-32},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Moment problems and polynomial approximation},
url = {http://eudml.org/doc/73407},
volume = {S5},
year = {1996},
}

TY - JOUR
AU - Berg, Christian
TI - Moment problems and polynomial approximation
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1996
PB - Université Paul Sabatier, Institut de Mathématiques
VL - S5
SP - 9
EP - 32
LA - eng
KW - Nevanlinna parametrization; moment problems; polynomial approximation; Carleman's condition
UR - http://eudml.org/doc/73407
ER -

References

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  1. [1] Akhiezer ( N.I. ) . — The classical moment problem, Oliver and Boyd, Edinburgh1965 . 
  2. [2] Al-Salam ( W.A.) and Carlitz ( L.) . — Some orthogonal q-polynomials . Math. Nachr., 30 ( 1965), pp. 47-61. Zbl0135.27802MR197804
  3. [3] Baillaud ( B. ) and Bourget ( H.) . — Correspondance d'Hermite et de Stieltjes I, II, Gauthier-Villars, Paris1905. 
  4. [4] Berg ( C.) . — Critical exponents for measures. in: Open problems, ed. W. Van Assche , J. Comput. Appl. Math., 48 (1993 ), p. 227. 
  5. [5] Berg ( C.) . — L2-approximation with respect to rotation invariant measures, Suppl. Rend. Circ. Mat. Palermo. Serie II, 33 (1993). pp. 211-217. Zbl0840.41004MR1295262
  6. [6] Berg ( C.) . — Indeterminate moment problems and the theory of entire functions, J. Comput. Appl. Math., 65 (1995), pp. 27-55. Zbl0853.44005MR1379118
  7. [7] Berg ( C.) . — Recent results about moment problems, in: Probability measures on groups and related structures XI, World Scientific , Singapore1995. Zbl0919.60005MR1414922
  8. [8] Berg ( C.) and Christensen ( J.P.R.) .— Density questions in the classical theory of moments, Ann. Inst. Fourier, 31, n° 3 (1981), pp. 99-114. Zbl0437.42007MR638619
  9. [9] Berg ( C.) and Christensen ( J.P.R.) .— Exposants critiques dans le problème des moments, C.R. Acad. Sci. Paris Série I, 296 ( 1983), pp. 661-663. Zbl0531.28008MR705685
  10. [10] Berg ( C.) and Duran ( A.J.) .— The index of determinacy for measures and the l2-norm of orthonormal polynomials, Trans. Amer. Math. Soc., 347 (1995), pp. 2795-2811. Zbl0863.42019MR1308001
  11. [11] Berg ( C.) and Duran ( A.J.) .— When does a discrete differential perturbation of a sequence of orthonormal polynomials belong to l2? J. Funct. Anal., 136 ( 1996), pp. 127-153. Zbl0867.46019MR1375156
  12. [12] Berg ( C.) and Duran ( A.J.) .— Orthogonal polynomials, L2-spaces and entire functions, Math. Scand. (to appear). Zbl0879.42015MR1452040
  13. [13] Berg ( C.) and Thill ( M.).— Rotation invariant moment problems , Acta Math.167 ( 1991), pp. 207-227. Zbl0744.44006MR1120603
  14. [14] Berg ( C.) and Thill ( M.) . — A density index for the Stieltjes moment problem, in: Orthogonal Polynomials and their Applications, ed. C. Brezinski, L. Gori and A. Ronveaux, IMACS Annals on computing and applied mathematics, 9 (1991), pp. 185-188. Zbl0830.44006MR1270229
  15. [15] Berg ( C.) and Valent ( G.). — The Nevalinna parametrization for some indeterminate Stieltjes moment problems associated with birth and death processes, Methods and Applications of Analysis, 1 (1994), pp. 169-209. Zbl0966.44500MR1291292
  16. [16] De Branges ( L. ) .— Hilbert spaces of entire functions , Prentice-Hall, Englewood Cliffs, N.J., 1968. Zbl0157.43301MR229011
  17. [17] Buchwalter ( H.) and Cassier ( G.) .— Mesures canoniques dans le problème classique des moments, Ann. Inst. Fourier, 34 (1984), pp. 45-52. Zbl0525.28002MR746493
  18. [18] Cassier ( G.) .— Mesures canoniques dans le problème classique des moments, C.R. Acad. Sci., 296, Série I (1984), pp. 717-719. Zbl0523.44009MR706666
  19. [19] Cassier ( G.) .— Problème des moments sur un compact de Rn et représentation de polynômes à plusieurs variables, J. Funct. Analysis, 58 (1984), pp. 254-266. Zbl0556.44006MR759099
  20. [20] Chihara ( T.S.) .— On indeterminate Hamburger moment problems, Pac. J. Math., 27 (1968), pp. 475-484. Zbl0167.41901MR238038
  21. [21] Chihara ( T.S.) .— Indeterminate symmetric moment problems, Math. Anal. Appl., 85 (1982), pp. 331-346. Zbl0485.44004MR649179
  22. [22] Choquet ( G.) .— Le problème des moments, Séminaire d'initiation à l'analyse (1962), Paris. 
  23. [23] Fuglede ( B.) .— The multidimensional moment problem , Expo. Math., 1 ( 1983), pp. 47-65. Zbl0514.44006MR693807
  24. [24] Hamburger ( H.) .— Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann., 81 (1920), pp. 235-319.; 82 (1921 ), pp. 120-164. 168-187. Zbl47.0427.04JFM47.0427.04
  25. [25] HAVIN (V. P.) et al. (editors) .— Linear and complex analysis problem book. 199 research problems , Lecture Notes in Mathematics, 1043, Springer, Berlin - Heidelberg - New York1984. Zbl0545.30038MR734178
  26. [26] Ismail ( M.E.H. ) .— A queueing model and a set of orthogonal polynomials, J. Math. Anal. Appl., 108 (1985), pp. 575-594. Zbl0579.60093MR793667
  27. [27] Ismail ( M.E.H. ) and Masson ( D.R.) .— Q-Hermite polynomials, biorthogonal rational functions and Q-beta integrals, Trans. Amer. Math. Soc., 346 (1994), pp. 63-116. Zbl0812.33012MR1264148
  28. [28] Kjeldsen ( T.H.) .— The early history of the moment problem, Historia Math., 20 (1993), pp. 19-44. Zbl0769.01008MR1205676
  29. [29] Koosis ( P.) .— The logarithmic integral I, Cambridge University Press, Cambridge1988. Zbl0665.30038MR961844
  30. [30] Naimark ( M.A.) .— Extremal spectral functions of a symmetric operator, Izv. Akad. Nauk. SSSR ser. matem., 11 (1947), pp. 327-344; Dokl. Akad. Nauk. SSSR, 54 (1946 ), pp. 7-9. Zbl0032.21501MR19220
  31. [31] Nevanlinna ( R.) .— Asymptotische Entwicklungen beschränkter Funktionen und das Stieltjessche Momentenproblem, Ann. Acad. Scient. Fennicae, (A), 18, n° 5 (1922), pp. 1-53. Zbl48.1226.02JFM48.1226.02
  32. [32] Petersen ( L.C.) .— On the relation between the multidimensional moment problem and the one-dimensional moment problem, Math. Scand., 51 (1982), pp. 361-366. Zbl0514.44007MR690537
  33. [33] Riesz ( M. ) .— Sur le problème des moment. Troisième Note, Arkiv för matematik, astronomi och fysik, 17, n° 16 (1923), pp. 1-52. JFM49.0195.01
  34. [34] Riesz ( M. ) .— Sur le problème des moments et le théorème de Parseval correspondant, Acta Litt. Ac. Sci. Szeged , 1 (1923), pp. 209-225. Zbl49.0708.02JFM49.0708.02
  35. [35] Schmüdgen ( K.) .— On determinacy notions for the two dimensional moment problem, Ark. Mat., 29 (1991), pp. 277-284. Zbl0762.44004MR1150378
  36. [36] Schmüdgen ( K.) .— The K-moment problem for compact semi-algebraic sets, Math. Ann., 289 (1991), pp. 203-206. Zbl0744.44008MR1092173
  37. [37] Sodin ( K. ) . — A note on the Hall-Mergelyan theme , Mathematical Physics, Analysis and Geometry (To appear). Zbl0872.44004
  38. [38] Stieltjes ( T.J.) .— Recherches sur les fractions continues , Annales de la Faculté des Sciences de Toulouse, 8 (1894), pp. 1-122; 9 (1895), pp. 5-47. MR1344720JFM25.0326.01

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