Heisenberg uniqueness pairs corresponding to a finite number of parallel lines

Bagchi, Sanjib

doi:10.1016/j.aim.2017.12.012

Cited by 7 publications

(3 citation statements)

References 11 publications

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“…Many examples of Heisenberg uniqueness pair have been obtained in the setting of the plane as well as in the higher dimensional Euclidean spaces. For more details see [1, 2, 5, 7–10, 13, 14, 16–20].…”

Section: Introductionmentioning

confidence: 99%

Heisenberg uniqueness pairs for the hyperbola

Giri

Rawat

2020

Bull. London Math. Soc.

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Let normalΓ be the hyperbola {false(x,yfalse)∈double-struckR2:xy=1} and Λβ be the lattice‐cross defined by normalΛβ=false(double-struckZ×{0}false)∪false({0}×βdouble-struckZfalse) in R2, where β is a positive real. A result of Hedenmalm and Montes‐Rodríguez says that (Γ,normalΛβ) is a Heisenberg uniqueness pair if and only if β⩽1. In this paper, we show that for a rational perturbation of Λβ, namely normalΛβθ=false(double-struckZ+false{θfalse}false)×false{0false}∪false{0false}×βdouble-struckZ,where θ=1/p,forsomep∈N and β is a positive real, the pair (Γ,normalΛβθ) is a Heisenberg uniqueness pair if and only if β⩽p.

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Section: Introductionmentioning

confidence: 99%

Heisenberg uniqueness pairs for the hyperbola

Giri

Rawat

2020

Bull. London Math. Soc.

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“…Sjölin [19] also studied the case where Γ is a parabola and Λ = Λ 1 ∪ Λ 1 , where Λ 1 and Λ 2 are subsets of two different straight lines, see also in [7]. When Γ corresponds to parallel lines or other algebraic curves, we refer to [1,5,6] and references therein. It's worth mentioning that Jaming and Kellay [14] transfer the question of whether (Γ, l 1 ∪ l 2 ) (l 1 , l 2 are two distinct lines) is a HUP to the study of a certain dynamical system on Γ generated by two lines.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Preface: Celebrating the 70th Anniversary of School of Mechanical Science and Engineering, Huazhong University of Science and Technology

Huang

Yin

2022

Sci. China Technol. Sci.

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The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some essential key properties of the weights of SFTR are explored for the first time. Based on these properties, we rigorously demonstrate the discrete energy decay property and maximum-principle preservation for the scheme. Numerical investigations show that the scheme can resolve the intrinsic initial singularity of such nonlinear fractional equations as tFAC equation on uniform meshes without any correction. Comparison with the classic fractional BDF2 and L2-1 σ method further validates the superiority of SFTR in solving the tFAC equation. Experiments concerning both discrete energy decay and discrete maximum-principle also verify the correctness of the theoretical results.

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“…A lot many examples of Heisenberg uniqueness pair have been obtained in the setting of the plane as well as in the higher dimensional Euclidean spaces. For more details see ( [1], [2], [5], [6], [7], [10], [11], [12], [13], [14], [15], [16]).…”

Section: Introductionmentioning

confidence: 99%

Heisenberg uniqueness pairs for some algebraic curves in the plane

Giri

Srivastava

2017

Advances in Mathematics

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Abstract. A Heisenberg uniqueness pair is a pair (Γ, Λ), where Γ is a curve and Λ is a set in R 2 such that whenever a finite Borel measure µ having support on Γ which is absolutely continuous with respect to the arc length on Γ satisfiesμ| Λ = 0, then it is identically 0. In this article, we investigate the Heisenberg uniqueness pairs corresponding to the spiral, hyperbola, circle and certain exponential curves. Further, we work out a characterization of the Heisenberg uniqueness pairs corresponding to four parallel lines. In the latter case, we observe a phenomenon of interlacing of three trigonometric polynomials.

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Heisenberg uniqueness pairs corresponding to a finite number of parallel lines

Abstract: Abstract. In this paper, we study the Heisenberg uniqueness pairs corresponding to a finite number of parallel lines Γ. We give a necessary condition and a sufficient condition for a subset Λ of R 2 so that (Γ, Λ) becomes a HUP.

Cited by 7 publications

References 11 publications

Heisenberg uniqueness pairs for the hyperbola

Heisenberg uniqueness pairs for the hyperbola

Preface: Celebrating the 70th Anniversary of School of Mechanical Science and Engineering, Huazhong University of Science and Technology

Heisenberg uniqueness pairs for some algebraic curves in the plane

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