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Quasi-diagonalization of Hankel operators and rational approximations of singular functions

Prof.
Dimitri Yafaev
Institution: 
Univ. Rennes
Location: 
A-134
Schedule: 
Wednesday, October 19, 2016 - 16:00 to 17:30
Abstract: 

We show that all Hankel operators are unitarily equivalent to pseudo-differential operators in L2 (R) with amplitudes a(x, y; ξ) of a very special structure:
a(x, y; ξ) = (cosh(πx))−1/2 s(ξ)(cosh(πy))−1/2
where the function s(ξ) is determined by the given Hankel operator. This result has numerous spectral applications. One of them (developed jointly with A. Pushnitski) concerns best rational approximations of functions with logarithmic singularities.

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