# What is the origin of the "Japanese bracket"?

In discussions of Sobolev spaces one often sees the Japanese bracket, $$\langle x \rangle = (1+|x|^2)^{1/2},$$ as useful shorthand.

(1) What was the first systematic usage of something like this shorthand?

(2) What is the origin of the specific phrase "Japanese bracket"?

(3) Why is it called the "Japanese bracket"? The answer to this may be obvious from the answers to either (1) or (2).