Interpolation, Schur Functions and Moment Problems

Schur analysis originates with a 1917 paper by Schur where he associated to a function analytic and contractive in the open unit disk a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often called reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others.

This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.

• Factorization
• Interpolation
• Inverse problems
• Matrix
• Moment problem
• Shift operator

• Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

  Daniel Alpay

• School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

  Israel Gohberg

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