Ergodic theorem

time average ” = ” space average

Ehrlings Lemma

TBA

Lp vs Lq

A function f may fail to be in Lp: either |f|^p blows up too rapidly near some point, or it fails to decay sufficiently rapidly at inifity.  For example, 1/x.

In the second part above,  it tells us a L^q function is a sum of an L^p function and an L^r function, if 0<p<q<r.

For more detalis,  I recommend Folland’s “Real Analysis” p185-186.

Holder imbedding

Notes on Hille-Yosida

Characterization of Sobolev spaces by Fourier transform

Haste makes waste

This is the awkard situation I am in.

But this is funny:

Foolproof: A Samplingof Mathematical FolkHumor

http://physics.csusb.edu/~prenteln/papers/notices.pdf