RECURSIVENESS, POSITIVITY, AND TRUNCATED

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RECURSIVENESS, POSITIVITY, AND TRUNCATED

Ial E. Curto,Lawrence A. Fialkow-1991-01-01

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TL;DRAbstract

Using elementary techniques from linear algebra, we de- scribe a recursire model for singular positive Hankel matrices. We then use this model to obtain necessary and sufficient conditions for existence or uniqueness of positive Borel measures which solve the truncated moment problems of Hamburger, Hausdorff and Stieltjes. We also present analogous results concerning Toeplitz matrices and the truncated trigonometric moment problem.

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Using elementary techniques from linear algebra, we de- scribe a recursire model for singular positive Hankel matrices. We then use this model to obtain necessary and sufficient conditions for existence or uniqueness of positive Borel measures which solve the truncated moment problems of Hamburger, Hausdorff and Stieltjes. We also present analogous results concerning Toeplitz matrices and the truncated trigonometric moment problem.

Keywords

MathematicsMoment (physics)UniquenessToeplitz matrixMoment problemPure mathematicsHausdorff spaceRiemann–Stieltjes integral

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