Approximate Identities

by Mr Sudarshan R. Gurjar (School of Mathematics, TIFR)

Tuesday 24 Jan 2012, 17:00 → 18:00 Asia/Kolkata

A-212 (STCS Seminar Room) (Colaba Campus)

I will explain the role played by infinitely differentiable functions with compact support on the real line. Suitably scaled such functions are very close (with respect to a suitable norm) to being identity elements for the binary operation of convolution of functions. If time permits, as an application I will sketch the proof of the famous Weirstrass approximation theorem in real analysis. Only knowledge of elementary calculus will be assumed.