Mathematics

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.