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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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$\textrm {BV}$-functions, positive-definite functions and moment problems
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by P. H. Maserick PDF
Trans. Amer. Math. Soc. 214 (1975), 137-152 Request permission

Abstract:

Let S be a commutative semigroup with identity 1 and involution. A complex valued function f on S is defined to be positive definite if ${\Pi _j}{\Delta _j}f(1) \geqslant 0$ where the ${\Delta _j}$’s belong to a certain class of linear sums of shift operators. For discrete groups the positive definite functions defined herein are shown to be the classically defined positive definite functions. An integral representation theorem is proved and necessary and sufficient conditions for a function to be the difference of two positive-definite functions, i.e. a BV-function, are given. Moreover the BV-function defined herein agrees with those previously defined for semilattices, with respect to the identity involution. Connections between the positive-definite functions and completely monotonic functions are discussed along with applications to moment problems.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 214 (1975), 137-152
  • MSC: Primary 43A35; Secondary 44A10, 44A50
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0380272-2
  • MathSciNet review: 0380272