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- W2069311130 abstract "It is well known that a line in R 2 is not a set of injectivity for the spherical means for odd functions about that line. We prove that any line passing through the origin is a set of injectivity for the twisted spherical means (TSM) for functions f ∈ L 2 ( C ) , whose each of spectral projection e 1 4 | z | 2 f × φ k is a polynomial. Then, we prove that any Coxeter system of even number of lines is a set of injectivity for the TSM for L p ( C ) , 1 ⩽ p ⩽ 2 . Further, we deduce that certain Coxeter system of even number of planes is a set of injectivity for the TSM for L p ( C n ) , 1 ⩽ p ⩽ 2 . We observe that a set S R 2 n − 1 × C is a set of injectivity for the TSM for a certain class of functions on C n + 1 ." @default.
- W2069311130 created "2016-06-24" @default.
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- W2069311130 date "2014-07-01" @default.
- W2069311130 modified "2023-09-29" @default.
- W2069311130 title "Coxeter system of lines and planes are sets of injectivity for the twisted spherical means" @default.
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- W2069311130 doi "https://doi.org/10.1016/j.jfa.2014.03.009" @default.
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