Skip to main content
SpringerLink
Log in

A Study of Probability Measures Through Commutators

  • Published:
Journal of Theoretical Probability Aims and scope Submit manuscript

Abstract

The first-order moments and two families of commutators are proven to determine uniquely the moments of a probability measure on ℝd. These families are the commutators between the annihilation and creation operators, and the commutators between the annihilation and preservation operators. An explicit method for recovering the moments from these commutators and first-order moments is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Accardi, L., Kuo, H.-H., Stan, A.I.: Characterization of probability measures through the canonically associated interacting Fock spaces. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 7(4), 485–505 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Accardi, L., Kuo, H.-H., Stan, A.I.: Moments and commutators of probability measures. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10(4), 591–612 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Asai, N., Kubo, I., Kuo, H.-H.: Multiplicative renormalization and generating functions I. Taiwan. J. Math. 7, 89–101 (2003)

    MATH  MathSciNet  Google Scholar 

  4. Asai, N., Kubo, I., Kuo, H.-H.: Generating functions of orthogonal polynomials and Szegö–Jacobi parameters. Probab. Math. Stat. 23, 273–291 (2003)

    MATH  MathSciNet  Google Scholar 

  5. Asai, N., Kubo, I., Kuo, H.-H.: Multiplicative renormalization and generating functions II. Taiwan. J. Math. 8, 593–628 (2004)

    MathSciNet  Google Scholar 

  6. Carleman, T.: Les Fonctions Quasi Analytiques. Collection Borel. Gauthier–Villars, Paris (1926)

    MATH  Google Scholar 

  7. Chihara, T.S.: An Introduction to Orthogonal Polynomials. Gordon & Breach, New York (1978)

    MATH  Google Scholar 

  8. Kubo, I., Kuo, H.-H., Namli, S.: Interpolation of Chebyshev polynomials and interacting Fock spaces. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9(3), 361–371 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Meixner, J.: Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion. J. Lond. Math. Soc. 9, 6–13 (1934)

    Article  MATH  Google Scholar 

  10. Szegö, M.: Orthogonal Polynomials. Coll. Publ., vol. 23. American Mathematical Society, Providence (1975)

    MATH  Google Scholar 

  11. Voiculescu, D.V., Dykema, K.J., Nica, A.: Free Random Variables. CRM Monograph Series, vol. 1. American Mathematical Society, Providence (1992)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The Ohio State University at Marion, 1465 Mount Vernon Avenue, Marion, OH, 43302, USA

    Aurel I. Stan

  2. Department of Mathematical Sciences, Shawnee State University, Portsmouth, OH, 45501, USA

    John J. Whitaker

Authors
  1. Aurel I. Stan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John J. Whitaker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aurel I. Stan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stan, A.I., Whitaker, J.J. A Study of Probability Measures Through Commutators. J Theor Probab 22, 123–145 (2009). https://doi.org/10.1007/s10959-008-0167-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10959-008-0167-5

Keywords

Mathematics Subject Classification (2000)

Search

Navigation