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The Required Condition of Hamburger moment problem for operators

Mr. Rajesh Saxena
Research Scholars, Jyoti Vidyapeeth Women’s University Jaipur, Rajasthan, India
Dr. Surendra kumar Srivastava
Associate Professor, Jyoti Vidyapeeth Women’s University Jaipur, Rajasthan, India
Online First: January 16, 2018
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Abstract

The Hamburger moment problem is an interesting question in analysis that deal Required Condition of Some bounded Sequence related to Hamburger problem for operator. Finally we discuss Hamburger moment problem operators satisfies are to sequences related to stieltjes moments sequence operator

Keyword : Hamburger moment Sequences and hamburger operator, stieltjes moments sequence operator

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Jan 16, 2018
Published
Jan 16, 2018
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References

1. T. Andô, “Truncated moment problems for operators,” Acta Scientiarum Mathematicarum, vol. 31, pp. 319–334, 1970. 2. J. W. Helton and M. Putinar, “Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization,” in Operator Theory, Structured Matrices, and Dilations, vol. 7, pp. 229–307, Theta, Bucharest, Romania, 2007. 3. F. J. Narcowich, “R-operators. II. On the approximation of certain operator-valued analytic functions and the Hermitian moment problem,” Indiana University Mathematics Journal, vol. 26, no. 3, pp. 483–513, 1977. 4. F.-H. Vasilescu, “Hamburger and Stieltjes moment problems in several variables,” Transactions of the American Mathematical Society, vol. 354, no. 3, pp. 1265–1278, 2002. 5. G. Choquet, Lectures on Analysis, vol. 2, Benjamin, New York, NY, USA, 1969 6. N.I. Akhiezer, The classical moment problem and some related questions in analysis, Oliver and Boyd, Edinburgh and London, 1965. MR 32:1518 7. C. Berg, J. P. R. Christensen, P. Ressel, Harmonic analysis on semigroups, SpringerVerlag, New York/Berlin/Heidelberg/Tokyo, 1984. MR 86b:43001 8. C. Berg and J. P. R. Christensen, Suites compl`etement d´efinies positives, majoration de Schur et le probl`eme des moments de Stieltjes en dimension k, C. R. Acad. Sc. Paris, S´erie I, 297 (1983), 45-48. MR 84k:44013 9. C. Berg and M. Thill, Rotation invariant moment problem, Acta Math. 167 (1991), 207-227. MR 92j:44004 10. R. E. Curto and L. A. Fialkow, Solution of the truncated complex moment problem for flat data, Memoirs of the A. M. S. Number 568, 1996. MR 96j:47009 11. R. E. Curto and L. A. Fialkow, Flat extensions of positive moment matrices: Recursively generated relations, Memoirs of the A. M. S. Number 648, 1998. MR 99d:47015 12. N. Dunford and J.T. Schwartz, Linear Operators, Part II, Interscience Publishers, New York/London/Sydney, 1963. MR 90g:47001b 13. A. Devinatz, Two parameter moment problems, Duke Math. J. 24 (1957), 481-498. MR 19:1047g 14. G.I. Eskin, A sufficient condition for the solvability of the moment problem in several dimensions, Transl. from Dokl. Akad. Nauk SSSR, 133 (1960), 540-543. MR 22:12394 15. B. Fuglede, The multidimensional moment problem, Expo. Math. 1 (1983), 47-65. MR 85g:44010
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References

1. T. Andô, “Truncated moment problems for operators,” Acta Scientiarum Mathematicarum, vol. 31, pp. 319–334, 1970.
2. J. W. Helton and M. Putinar, “Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization,” in Operator Theory, Structured Matrices, and Dilations, vol. 7, pp. 229–307, Theta, Bucharest, Romania, 2007.
3. F. J. Narcowich, “R-operators. II. On the approximation of certain operator-valued analytic functions and the Hermitian moment problem,” Indiana University Mathematics Journal, vol. 26, no. 3, pp. 483–513, 1977.
4. F.-H. Vasilescu, “Hamburger and Stieltjes moment problems in several variables,” Transactions of the American Mathematical Society, vol. 354, no. 3, pp. 1265–1278, 2002.
5. G. Choquet, Lectures on Analysis, vol. 2, Benjamin, New York, NY, USA, 1969
6. N.I. Akhiezer, The classical moment problem and some related questions in analysis, Oliver and Boyd, Edinburgh and London, 1965. MR 32:1518
7. C. Berg, J. P. R. Christensen, P. Ressel, Harmonic analysis on semigroups, SpringerVerlag, New York/Berlin/Heidelberg/Tokyo, 1984. MR 86b:43001
8. C. Berg and J. P. R. Christensen, Suites compl`etement d´efinies positives, majoration de Schur et le probl`eme des moments de Stieltjes en dimension k, C. R. Acad. Sc. Paris, S´erie I, 297 (1983), 45-48. MR 84k:44013
9. C. Berg and M. Thill, Rotation invariant moment problem, Acta Math. 167 (1991), 207-227. MR 92j:44004
10. R. E. Curto and L. A. Fialkow, Solution of the truncated complex moment problem for flat data, Memoirs of the A. M. S. Number 568, 1996. MR 96j:47009
11. R. E. Curto and L. A. Fialkow, Flat extensions of positive moment matrices: Recursively generated relations, Memoirs of the A. M. S. Number 648, 1998. MR 99d:47015
12. N. Dunford and J.T. Schwartz, Linear Operators, Part II, Interscience Publishers, New York/London/Sydney, 1963. MR 90g:47001b
13. A. Devinatz, Two parameter moment problems, Duke Math. J. 24 (1957), 481-498. MR 19:1047g
14. G.I. Eskin, A sufficient condition for the solvability of the moment problem in several dimensions, Transl. from Dokl. Akad. Nauk SSSR, 133 (1960), 540-543. MR 22:12394
15. B. Fuglede, The multidimensional moment problem, Expo. Math. 1 (1983), 47-65. MR 85g:44010
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