Estimates for the SVD of the Truncated Fourier Transform on $$L^2(\cosh (b|\cdot |))$$ and Stable Analytic Continuation

The Fourier transform truncated on $$[-c,c]$$ has for a long time been analyzed as acting $$L^2(-1/b,1/b)$$ into $$L^2(-1,1)$$ and its right-singular vectors are the prolate spheroidal wave functions. This paper considers operator defined larger space $$L^2(\cosh (b|\cdot |))$$ which it remains injective. main purpose is (1) to provide nonasymptotic upper lower bounds singular values with similar qualitative behavior in m (the index), b, c (2) derive sup-norm of Finally, we propose numerical method compute SVD. These fundamental results Gaillac Gautier (Adaptive estimation linear random coefficients model when regressors have limited variation, Bernoulli, arXiv:1905.06584 ). an illustrative example analytic continuation nonbandlimited functions function observed error interval.