Interpolation Theory

Contains the notes of the courses in Interpolation Theory that the author gave at Scuola Normale in 1998 and in 1999, illustrating the principles of Interpolation Theory aiming at simplification rather than at generality.

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This booklet contains the notes of the courses in Interpolation Theory that I gave at Scuola Normale in 1998 and in 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In these lectures I tried to illustrate the principles of Interpolation Theory aiming at simplification rather than at generality. I reduced the abstract theory as far as possible, and gave many examples and applications, especially to partial differential operators and partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.