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math.CA2022
Córdoba's differentation theorem: revisited
Ángel D. Martínez
In this paper we prove an exponential covering lemma implying the three dimensional case of a well-known conjecture formulated by A. Zygmund circa 1935 and solved by A. Córdoba in…
math.CA2022
Distribution symmetry of toral eigenfunctions
Ángel D. Martínez, Francisco Torres de Lizaur
In this paper we study a number of conjectures on the behavior of the value distribution of eigenfunctions. On the two dimensional torus we observe that the symmetry conjecture hol…
math.CA2022
Eigenfunction maxima and spherical means
Ángel D. Martínez
The eigenfunctions of the Laplacian are a central object from the realms of analytic number theory to geometric analysis. We prove that Hörmander - estimates are e…