Localized Bernstein bounds for functions in complex rectangles enable Erdős-type lower bounds on Lebesgue constants for interpolation on shorter intervals and their integrals.
Runge, ¨Uber empirische Funktionen und die Interpolation zwischen ¨ aquidistanten Ordinaten, Zeitschrift f¨ ur Mathematik und Physik46(1901), 224–243
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Local Bernstein theory, and lower bounds for Lebesgue constants
Localized Bernstein bounds for functions in complex rectangles enable Erdős-type lower bounds on Lebesgue constants for interpolation on shorter intervals and their integrals.