Some positive definite functions on sets and their application to the Ising model
✍ Scribed by Ole J. Heilmann; Daniel J. Kleitman; Elliott H. Lieb; Seymour Sherman
- Book ID
- 107748109
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 635 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
Let f be a positive definite function on a locally compact abelian group G. In [3] we showed that measurability of 1 on an open neighbourhood of the zero implies measurability of f on G. As a main tool we used a result about the support of f [3, Th. I]. The aim of this note is to simplify the proof
We show the monotonic properties of canonical correlation coecients and the concave±convex properties of some of their functions with respect to some elements of the variance±covariance corresponding to them, and then use these results to discuss the monotonic and concave±convex properties of the re