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Optimization problems related to the John uniqueness theorem


Authors: V. V. Volchkov and Vit. V. Volchkov
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 21 (2009), nomer 5.
Journal: St. Petersburg Math. J. 21 (2010), 705-729
MSC (2010): Primary 44A35
DOI: https://doi.org/10.1090/S1061-0022-2010-01113-0
Published electronically: July 14, 2010
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Abstract | References | Similar Articles | Additional Information

Abstract: The spectrum structure problem is considered for a distribution that is periodic in the mean and satisfies uniqueness conditions of John type. The solution of this problem is obtained for a wide class of distributions on arbitrary Riemannian two-point-homogeneous spaces.


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Additional Information

V. V. Volchkov
Affiliation: Donetsk National University, 3 Malyshko Street, Donetsk 83053, Ukraine
Email: valeriyvolchkov@gmail.com

Vit. V. Volchkov
Affiliation: Donetsk National University, 3 Malyshko Street, Donetsk 83053, Ukraine
Email: volchkov@univ.donetsk.ua

DOI: https://doi.org/10.1090/S1061-0022-2010-01113-0
Keywords: Two-point-homogeneous spaces, spherical harmonics, periodicity in the mean, John uniqueness theorem
Received by editor(s): June 16, 2008
Published electronically: July 14, 2010
Article copyright: © Copyright 2010 American Mathematical Society