# Extreme positive definite double sequences which are not moment sequences.

Collectanea Mathematica (2003)

- Volume: 54, Issue: 1, page 87-98
- ISSN: 0010-0757

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topBisgaard, Torben Maack. "Extreme positive definite double sequences which are not moment sequences.." Collectanea Mathematica 54.1 (2003): 87-98. <http://eudml.org/doc/43026>.

@article{Bisgaard2003,

abstract = {From the fact that the two-dimensional moment problem is not always solvable, we can deduce that there must be extreme ray generators of the cone of positive definite double sequences which are nor moment sequences. Such an argument does not lead to specific examples. In this paper it is shown how specific examples can be constructed if one is given an example of an N-extremal indeterminate measure in the one-dimensional moment problem (such examples exist in the literature). Konrad Schmüdgen had an example similar to ours.},

author = {Bisgaard, Torben Maack},

journal = {Collectanea Mathematica},

keywords = {Funciones definidas positivas; Series dobles; Problemas de momento; countable abelian semigroup with zero; positive definite function; character; moment function; semiperfect semigroup; determinate moment sequence; indeterminate moment sequence; determinate measure; indeterminate measure; -extremal measure},

language = {eng},

number = {1},

pages = {87-98},

title = {Extreme positive definite double sequences which are not moment sequences.},

url = {http://eudml.org/doc/43026},

volume = {54},

year = {2003},

}

TY - JOUR

AU - Bisgaard, Torben Maack

TI - Extreme positive definite double sequences which are not moment sequences.

JO - Collectanea Mathematica

PY - 2003

VL - 54

IS - 1

SP - 87

EP - 98

AB - From the fact that the two-dimensional moment problem is not always solvable, we can deduce that there must be extreme ray generators of the cone of positive definite double sequences which are nor moment sequences. Such an argument does not lead to specific examples. In this paper it is shown how specific examples can be constructed if one is given an example of an N-extremal indeterminate measure in the one-dimensional moment problem (such examples exist in the literature). Konrad Schmüdgen had an example similar to ours.

LA - eng

KW - Funciones definidas positivas; Series dobles; Problemas de momento; countable abelian semigroup with zero; positive definite function; character; moment function; semiperfect semigroup; determinate moment sequence; indeterminate moment sequence; determinate measure; indeterminate measure; -extremal measure

UR - http://eudml.org/doc/43026

ER -

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