70 citations · 486 across the 82 of their papers we have counts for
6 papers · 1 filter
On nodal sets and nodal domains on S^2 and R^2
Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili
We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S^2. We also construct a solution of the equa…
Zeros of eigenfunctions of some anharmonic oscillators
Alexandre Eremenko, Andrei Gabrielov, Boris Shapiro
We study eigenfunctions of Schrodinger operators -y"+Py on the real line with zero boundary conditions, whose potentials P are real even polynomials with positive leading coefficie…
Direct singularities and completely invariant domains of entire functions
Walter Bergweiler, Alexandre Eremenko
Let f be a transcendental entire function that omits a complex value a. We show that for every simply connected region D that does not contain a the full preimage of D is disconnec…
Landau's theorem for holomorphic curves in projective space and the Kobayashi metric on hyperplane complements
William Cherry, Alexandre Eremenko
We prove an effective version of a theorem of Dufresnoy: For any set of 2n+1 hyperplanes in general position in n-dimensional complex projective space, we find an explicit constant…
A Markov-type inequality for arbitrary plane continua
Alexandre Eremenko
A version of Markov's estimate for the derivative of a polynomial is proved with the interval [-1,1] replaced by an arbitrary continuum in the complex plane.
Uniform approximation of sgn(x) by polynomials and entire functions
Alexandre Eremenko, Peter Yuditskii
We study the best uniform approximation by polynomials of fixed degree of the function sgn(x) on the union of two intervals symmetric with respect to the origin. We obtain precise…