27 citations · 157 across the 50 of their papers we have counts for
6 papers · 1 filter
On the Sign Distributions of Hilbert Space Frames
Nikolai Nikolski, Alexander Volberg
We show that the positive and negative parts of any frame in a real space with respect to a continuous measure have both "infinite masses": 1) alw…
Counting eigenvalues of Schrödinger operator with complex fast decreasing potential
Alexander Borichev, Rupert Frank, Alexander Volberg
We give a sharp estimate of the number of zeros of analytic functions in the unit disc belonging to analytic quasianalytic Carleman--Gevrey classes. As an application, we estimate…
Improving constant in end-point Poincaré inequality on Hamming cube
Paata Ivanisvili, Dong Li, Ramon van Handel +1
We improve the constant in -Poincaré inequality on Hamming cube. For Gaussian space the sharp constant in inequality is known, and it is .…
Bi-parameter embedding and measures with restriction energy condition
Nicola Arcozzi, Irina Holmes, Pavel Mozolyako +1
Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, and Giulia Sarfatti recently gave the proof of a bi-parameter Carleson embedding theorem. Their proof uses heavily the notion…
Bellman function sitting on a tree
Nicola Arcozzi, Irina Holmes, Pavel Mozolyako +1
In this note we give a proof-by-formula of certain important embedding inequalities on dyadic tree. This is done with the help of Bellman function. We also consider the case of a b…
Poincaré type and spectral gap inequalities with fractional Laplacians on Hamming cube
Dong Li, Alexander Volberg
We prove here some dimension free Poincaré-type inequalities on Hamming cube for functions with different spectral properties and for fractional Laplacians. In this note the main a…