# Subduals and tensor products of spaces of harmonic functions

• Volume: 24, Issue: 3, page 119-144
• ISSN: 0373-0956

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## Abstract

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Working in the axiomatic potential theory of M. Brelot, a description of the subdual of the vector space generated by the cone of positive harmonic functions on a harmonic space, $\Omega$, is given. Under certain hypothesis this is seen to be a function space on the Martin boundary of $\Omega$. Some ancillary results are proved. Next, it is shown, using this result and the theory of tensor products of simplexes, that the cone of positive separately harmonic functions is the tensor product of the cones of positive harmonic functions on the factor spaces. With this theorem as a starting point it is demonstrated that by using tensor product techniques whenever possible many proofs of results in the theory of separately harmonic functions can be simplified and new results obtained.

## How to cite

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Reay, Ian. "Subduals and tensor products of spaces of harmonic functions." Annales de l'institut Fourier 24.3 (1974): 119-144. <http://eudml.org/doc/74179>.

@article{Reay1974,
abstract = {Working in the axiomatic potential theory of M. Brelot, a description of the subdual of the vector space generated by the cone of positive harmonic functions on a harmonic space, $\Omega$, is given. Under certain hypothesis this is seen to be a function space on the Martin boundary of $\Omega$. Some ancillary results are proved. Next, it is shown, using this result and the theory of tensor products of simplexes, that the cone of positive separately harmonic functions is the tensor product of the cones of positive harmonic functions on the factor spaces. With this theorem as a starting point it is demonstrated that by using tensor product techniques whenever possible many proofs of results in the theory of separately harmonic functions can be simplified and new results obtained.},
author = {Reay, Ian},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {119-144},
publisher = {Association des Annales de l'Institut Fourier},
title = {Subduals and tensor products of spaces of harmonic functions},
url = {http://eudml.org/doc/74179},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Reay, Ian
TI - Subduals and tensor products of spaces of harmonic functions
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 3
SP - 119
EP - 144
AB - Working in the axiomatic potential theory of M. Brelot, a description of the subdual of the vector space generated by the cone of positive harmonic functions on a harmonic space, $\Omega$, is given. Under certain hypothesis this is seen to be a function space on the Martin boundary of $\Omega$. Some ancillary results are proved. Next, it is shown, using this result and the theory of tensor products of simplexes, that the cone of positive separately harmonic functions is the tensor product of the cones of positive harmonic functions on the factor spaces. With this theorem as a starting point it is demonstrated that by using tensor product techniques whenever possible many proofs of results in the theory of separately harmonic functions can be simplified and new results obtained.
LA - eng
UR - http://eudml.org/doc/74179
ER -

## References

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