Measure, Integration & Real Analysis · Problem 8C.19

Real and Complex Measures — Sheldon Axler

Mathematics — Measure Theory · polynomial-reproducing-kernel

Problem

Find the polynomial

g

of degree at most 4 such that

f\!\left(\tfrac{1}{2}\right) = \int_0^1 f\, g

for every polynomial

f

of degree at most 4.