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In the field of mathematical analysis, an interpolation space is a space which lies "in between" two other Banach spaces. The main applications are in Sobolev spaces, where spaces of functions that have a noninteger number of derivatives are interpolated from the spaces of functions with integer number of derivatives. ==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 and also on a certain space , then it is also continuous on the space , for any intermediate between and . In other words, is a space which is intermediate between and . 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,〔The seminal papers in this direction are and .〕 real interpolation,〔first defined in , developed in , with notation slightly different (and more complicated, with four parameters instead of two) from today's notation. It was put later in today's form in , and .〕 as well as other tools (see e.g. fractional derivative). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Interpolation space」の詳細全文を読む スポンサード リンク
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