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Conical Uniqueness Sets for the Spherical Radon Transform
Author(s) -
Agranovsky M. L.,
Volchkov V. V.,
Zalcman L. A.
Publication year - 1999
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/s0024609398005396
Subject(s) - mathematics , uniqueness , conical surface , radon transform , homogeneous , mathematics subject classification , zero (linguistics) , mathematical analysis , polynomial , set (abstract data type) , spherical harmonics , harmonic function , homogeneous polynomial , pure mathematics , combinatorics , geometry , matrix polynomial , linguistics , philosophy , computer science , programming language
Let K be a cone in R n . Then K is a uniqueness set for the spherical Radon transform if and only if it is not contained in the zero set of any (nontrivial) homogeneous harmonic polynomial. A local version of this result is also proved. 1991 Mathematics Subject Classification 44A12.