Skip to main content
SpringerLink
Log in

A generalized moment problem

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Let {λ n} (n≧0) satisfy (1.1) we are considering the following problems: What are the necessary and sufficient conditions on a sequence {μn} (n≧0) in order that it should possess the representation (1.2) wherea(t) is of bounded variation or the representation (1.3) wheref(t) ∈L M[0, 1] orf(t) is essentially bounded.

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

Bibliography

  1. D. L. Berman,Application of interpolatory polynomial operators to solve the moment problem, Ukrain Math. Ž14 (1963), 184–190.

    Article  Google Scholar 

  2. K. Endl,On system of linear inequalities in infinitely many variables and generalized Hausdorff means, Math. Zeit.82 (1963), 1–7.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Hausdorff,Summationsmethoden und momentenfolgen I, II, Math. Zeit.9 (1921), 74–109, 280–299.

    Article  MathSciNet  Google Scholar 

  4. ——,Momentenproblem für ein endliches interval. Math. Zeit.16, (1923), 220–248.

    Article  MathSciNet  Google Scholar 

  5. A. Jakimovski,The product of summability methods; new classes of transformations and their properties II, Technical (Scientific) Note No. 4 Contract No. AF 61 (052)-187, August 1959.

  6. M. A. Krasnosel’skii and Ya. B. Rutickii,Convex functions and Orlicz spaces, Translated by Leo F. Boron. P. Noordhoff Ltd. — Groningen — The Netherlands 1961.

  7. G. G. Lorentz,Bernstein polynomials, Toronto, 1953.

  8. Yu. Medvedev,Generalization of a theorem of F. Riesz, Uspehi Matem. Nauk,8 (1953) 115–118.

    MATH  Google Scholar 

  9. I. J. Schoenberg,On finite rowed systems of linear inequalities in infinitely many variables, Trans. Amer. Math. Soc.34 (1932), 594–619.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. V. Widder,The Laplace transform, Princeton, 1946.

Download references

Author information

Authors and Affiliations

  1. Tel-Aviv University, Tel-Aviv, Israel

    D. Leviatan

Authors
  1. D. Leviatan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leviatan, D. A generalized moment problem. Israel J. Math. 5, 97–103 (1967). https://doi.org/10.1007/BF02771628

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02771628

Keywords

Search

Navigation