Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle | Zendy

Semyon Dyatlov | Zendy

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Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle

Author(s) -

Semyon Dyatlov

Publication year - 2018

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.654

Subject(s) - eigenfunction , bounded function , fractal , eigenvalues and eigenvectors , mathematics , norm (philosophy) , laplace operator , constant (computer programming) , set (abstract data type) , mathematical analysis , pure mathematics , open set , computer science , physics , epistemology , philosophy , quantum mechanics , programming language

This expository article, written for the proceedings of the Journ\'ees EDP (Roscoff, June 2017), presents recent work joint with Jean Bourgain [arXiv:1612.09040] and Long Jin [arXiv:1705.05019]. We in particular show that eigenfunctions of the Laplacian on hyperbolic surfaces are bounded from below in $L^2$ norm on each nonempty open set, by a constant depending on the set but not on the eigenvalue.

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