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Schur Analysis

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 256))

Abstract

As discussed in Chapter 1, functions analytic and contractive in the open unit disk, the Schur functions, are part of classical mathematics, as is illustrated by the works of Schur [261, 262], Takagi [270, 271], and Bloch [98], to name a few. They play an important role in numerous areas of mathematics, and can be characterized in a number of ways. By the name Schur analysis one means a collection of problems pertaining to Schur functions in function theory, operator theory, and related fields. In this chapter we gather the main aspects in this setting useful to the reader in preparation for the quaternionic generalization presented in this book.

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Alpay, D., Colombo, F., Sabadini, I. (2016). Schur Analysis. In: Slice Hyperholomorphic Schur Analysis. Operator Theory: Advances and Applications, vol 256. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-42514-6_3

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