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Creators/Authors contains: "Kim, Elena"

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  1. ; (, Physica Scripta)
    Abstract We studyℓ∞norms ofℓ2-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Biévre in F Bonechi and S De Bièvre (2000,Communications in Mathematical Physics,211, 659–686)) we show that there exists a sequence of eigenfunctionsuwith ∥ u ∥ ∞ ≳ log N − 1 / 2 . For general eigenfunctions we show the upper bound ∥ u ∥ ∞ ≲ log N − 1 / 2 . Here the semiclassical parameter is h = 2 π N − 1 . Our upper bound is analogous to the one proved by Bérard in P Bérard (1977,Mathematische Zeitschrift,155, 249-276) for compact Riemannian manifolds without conjugate points. 
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  2. ; ; ; (, Journal of Mathematical Analysis and Applications)
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  3. ; (, Journal of Number Theory)
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  4. ; ; (, Complex Analysis and its Synergies)
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  5. ; ; ; (, New York journal of mathematics)
    The complex Green operator $$\mathcal{G}$$ on CR manifolds is the inverse of the Kohn-Laplacian $$\square_b$$ on the orthogonal complement of its kernel. In this note, we prove Schatten and Sobolev estimates for $$\mathcal{G}$$ on the unit sphere $$\mathbb{S}^{2n-1}\subset \mathbb{C}^n$$. We obtain these estimates by using the spectrum of $$\boxb$$ and the asymptotics of the eigenvalues of the usual Laplace-Beltrami operator. 
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  6. ; ; (, Operators and Matrices)
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