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The Finite Subsets of Z 2 Having the Extension Property
Author(s) -
Bakonyi Mihály,
Nævdal Geir
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001496
Subject(s) - extension (predicate logic) , property (philosophy) , mathematics , measure (data warehouse) , combinatorics , finite set , pure mathematics , discrete mathematics , mathematical analysis , computer science , philosophy , epistemology , database , programming language
The paper considers finite subsets Λ ⊂ Z d which possess the extension property, namely that every collection { c k } k ∈Λ−Λ of complex numbers which is positive definite with respect to Λ is the restriction of the Fourier coefficients of some positive measure on T d . All finite subsets of Z 2 which possess the extension property are described.