Publications

@techreport{lederman_stability_2016,
title = {Stability Estimates for Truncated Fourier and Laplace Transforms},
author = {Roy R Lederman and Stefan Steinerberger},
url = {https://arxiv.org/abs/1605.03866v1},
year = {2016},
date = {2016-05-01},
urldate = {2020-08-13},
number = {arXiv:1605.03866},
abstract = {We prove sharp stability estimates for the Truncated Laplace Transform and
Truncated Fourier Transform. The argument combines an approach recently
introduced by Alaifari, Pierce and the second author for the truncated Hilbert
transform with classical results of Bertero, Grünbaum, Landau, Pollak and
Slepian. In particular, we prove there is a universal constant $c textgreater0$ such that
for all $f textbackslashin Ltextasciicircum2(textbackslashmathbbR)$ with compact support in $[-1,1]$ normalized to $textbackslashtextbarftextbackslashtextbar_Ltextasciicircum2[-1,1] = 1$ $$ textbackslashint_-1textasciicircum1textbartextbackslashwidehatf(ξ)textbartextasciicircum2dξ textbackslashgtrsim
textbackslashleft(ctextbackslashlefttextbackslashtextbarf_x textbackslashrighttextbackslashtextbar_Ltextasciicircum2[-1,1] textbackslashright)textasciicircumvphantom- ctextbackslashlefttextbackslashtextbarf_x
textbackslashrighttextbackslashtextbar_Ltextasciicircum2[-1,1]vphantom$$ The inequality is sharp in the sense that there is an
infinite sequence of orthonormal counterexamples if $c$ is chosen too small.
The question whether and to which extent similar inequalities hold for generic
families of integral operators remains open.},
keywords = {Laplace Transform},
pubstate = {published},
tppubtype = {techreport}
}

@techreport{lederman_analytical_2014,
title = {On the Analytical and Numerical Properties of the Truncated Laplace Transform},
author = {Roy R Lederman},
year = {2014},
date = {2014-01-01},
number = {YALEU/DCS/TR-1490},
pages = {82},
institution = {Yale CS},
keywords = {Algorithms, Laplace Transform, Numerical Analysis},
pubstate = {published},
tppubtype = {techreport}
}