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The Product of Minimal Functions is Minimal
Author(s) -
Taylor J. C.
Publication year - 1990
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/22.5.499
Subject(s) - mathematics , brownian motion , product (mathematics) , eigenfunction , simple (philosophy) , pure mathematics , manifold (fluid mechanics) , mathematical analysis , geometry , physics , eigenvalues and eigenvectors , statistics , mechanical engineering , philosophy , epistemology , quantum mechanics , engineering
Using Doob's h ‐processes, a simple proof is given of a result of Freire: every product of minimal eigenfunctions for Brownian motions on each one of a product of complete Riemannian manifolds is itself minimal for the Brownian motion on the product manifold.