Geodesic
The Generalized Moment Problem Associated with Correlation Measures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 4, pp. 86-91

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The classical power moment problem can be viewed as a theory of spectral representations of a positive functional on some classical commutative algebra with involution. We generalize this approach to the case in which the algebra is a special commutative algebra of functions on the space of multiple finite configurations. If the above-mentioned functional is generated by a measure on the space of finite ordinary configurations, then this measure is the correlation measure for a measure on the space of infinite configurations. The positiveness of the functional gives conditions for the measure to be a correlation measure.
Mots-clés : convolution
Keywords: positive functional, generalized joint eigenvector, correlation measure. 
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     author = {Yu. M. Berezanskii},
     title = {The {Generalized} {Moment} {Problem} {Associated} with {Correlation} {Measures}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2003_37_4_a11/}
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Yu. M. Berezanskii. The Generalized Moment Problem Associated with Correlation Measures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 4, pp. 86-91. http://geodesic.mathdoc.fr/item/FAA_2003_37_4_a11/