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

I was not easily able to find information about this term.

(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).

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