History
The theory of interpolation of vector spaces began by an observation of Józef Marcinkiewicz, later generalized and now known as the Riesz-Thorin theorem. In simple terms, if a linear function is continuous on a certain space Lp and also on a certain space Lq, then it is also continuous on the space Lr, for any intermediate r between p and q. In other words, Lr is a space which is intermediate between Lp and Lq.
In the development of Sobolev spaces, it became clear that the trace spaces were not any of the usual function spaces (with integer number of derivatives), and Jacques-Louis Lions discovered that indeed these trace spaces were constituted of functions that have a noninteger degree of differentiability.
Many methods were designed to generate such spaces of functions, including the Fourier transform, complex interpolation, real interpolation, as well as other tools (see e.g. fractional derivative).
Read more about this topic: Interpolation Space
Famous quotes containing the word history:
“There has never been in history another such culture as the Western civilization M a culture which has practiced the belief that the physical and social environment of man is subject to rational manipulation and that history is subject to the will and action of man; whereas central to the traditional cultures of the rivals of Western civilization, those of Africa and Asia, is a belief that it is environment that dominates man.”
—Ishmael Reed (b. 1938)
“Well, for us, in history where goodness is a rare pearl, he who was good almost takes precedence over he who was great.”
—Victor Hugo (1802–1885)
“Racism is an ism to which everyone in the world today is exposed; for or against, we must take sides. And the history of the future will differ according to the decision which we make.”
—Ruth Benedict (1887–1948)