81 citations · 202 across the 43 of their papers we have counts for
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Subordination by orthogonal martingales in and zeros of Laguerre polynomials
Alexander Borichev, Prabhu Janakiraman, Alexander Volberg
In this paper we address the question of finding the best -norm constant for martingale transforms with one-sided orthogonality. We consider two martingales on a probability s…
Weighted exponential approximation and non-classical orthogonal spectral measures
Alexander Borichev, Mikhail Sodin
A long-standing open problem in harmonic analysis is: given a non-negative measure on , find the infimal width of frequencies needed to approximate any function in $…
Boundary uniqueness of harmonic functions and spectral subspaces of operator groups
Alexander Borichev, Yuri Tomilov
We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral s…
On Burkholder function for orthogonal martingales and zeros of Legendre polynomials
Alexander Borichev, Prabhu Janakiraman, Alexander Volberg
Burkholder obtained a sharp estimate of $\E|W|^p$ via $\E|Z|^p$, where is a martingale transform of , or, in other words, for martingales differentially subordinated to…
Stable and Norm-stable Invariant Subspaces
Alexander Borichev, Don Hadwin, Hassan Yousefi
We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then th…