Non-harmonic cones are sets of injectivity for the twisted spherical means on ℂⁿ

Srivastava, Rajesh K.

doi:10.1090/tran/6488

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Some Preliminaries1

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2018

2022

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Cited by 4 publications

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“…We say a complex cone is non-harmonic if it is not contained in the zero set of any bi-graded homogeneous harmonic polynomial on C n . An example of a non-harmonic complex cone was produced by the author (see [28]). The zero set of the polynomial H(z) = az 1 z2 + |z| 2 , where a = 0 and z ∈ C n is a complex cone which is not contained in the zero set of any bi-graded homogeneous harmonic polynomial.…”

Section: Some Preliminariesmentioning

confidence: 99%

Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg group

Ghosh

Srivastava

2018

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In this article, we prove that (non-harmonic cone, unit sphere) is a Heisenberg uniqueness pair for the symplectic Fourier transform on C n . And we derive that a sphere whose radius is not contained in the zero sets of the Laguerre polynomials is a determining set for the spectral projections corresponding to the finite measure supported on the unit sphere. Further, we prove that if the Fourier transform of a certain finitely supported function on step two nilpotent Lie groups is of arbitrary finite rank, then the function must be zero.

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Section: Some Preliminariesmentioning

confidence: 99%