Stieltjes moment sequences

and positive definite matrix sequences

Author:
Torben Maack Bisgaard

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3227-3237

MSC (1991):
Primary 43A35, 44A60, 47-xx, 60-xx

DOI:
https://doi.org/10.1090/S0002-9939-98-04373-1

MathSciNet review:
1452793

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Abstract | References | Similar Articles | Additional Information

Abstract: For a certain constant (a little less than ), every function satisfying , , is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence there is a positive definite matrix sequence which is not of positive type and which satisfies , . For a certain constant (a little greater than ), for every function satisfying , , there is a convolution semigroup of measures on , with moments of all orders, such that , , and for every such convolution semigroup the measure is Stieltjes indeterminate for all .

**1.**N. I. Akhiezer,*The Classical Moment Problem*, Oliver & Boyd, Edinburgh and London, 1965.**2.**T. M. Bisgaard, Positive definite operator sequences,*Proc. Amer. Math. Soc.***121**(1994), 1185-1191. MR**94j:43004****3.**T. M. Bisgaard and Z. Sasvári, On the positive definiteness of certain functions,*Math. Nachr.***186**(1997), 81-99. CMP**97:16****4.**R. P. Boas, The Stieltjes moment problem for functions of bounded variation,*Bull. Amer. Math. Soc.***45**(1939), 399-404.

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Additional Information

**Torben Maack Bisgaard**

Affiliation:
Nandrupsvej 7 st. th., DK-2000 Frederiksberg C, Denmark

DOI:
https://doi.org/10.1090/S0002-9939-98-04373-1

Keywords:
Stieltjes moment sequence,
indeterminate,
moment sequence,
positive definite,
positive type,
convolution semigroup

Received by editor(s):
July 15, 1996

Received by editor(s) in revised form:
February 24, 1997

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society