41 citations · 243 across the 26 of their papers we have counts for
14 papers · 1 filter
Dynamical versions of Hardy's uncertainty principle: A survey
Aingeru Fernández-Bertolin, Eugenia Malinnikova
The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. The textbook proof of the result, as well as one of…
On a Bernstein inequality for eigenfunctions
Stefano Decio, Eugenia Malinnikova
Let be an eigenfunction of the Laplace-Beltrami operator on a smooth compact Riemannian manifold , i.e., . We show that satisfies a local Berns…
The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions
A. Logunov, E. Malinnikova, N. Nadirashvili +1
Let be a bounded domain in with boundary and let be a Dirichlet Laplace eigenfunction in with eigenvalue . We show that the -dimensio…
On the three ball theorem for solutions of the Helmholtz equation
Stine Marie Berge, Eugenia Malinnikova
Let be a solution of the Helmholtz equation with the wave number , , on a small ball in either , , or . For a fix…
Local version of Courant's nodal domain theorem
S. Chanillo, A. Logunov, E. Malinnikova +1
Let be a closed Riemannian manifold, where g is -smooth metric. Consider the sequence of eigenfunctions of the Laplace operator on M. Let be a ball on .…
Review of Yau's conjecture on zero sets of Laplace eigenfunctions
Alexander Logunov, Eugenia Malinnikova
This is a review of old and new results and methods related to the Yau conjecture on the zero set of Laplace eigenfunctions. The review accompanies two lectures given at the confer…