Download E-books Orthogonal Rational Functions (Cambridge Monographs on Applied and Computational Mathematics) PDF

By Pablo Gonzalez-Vera, Erik Hendriksen, Olav Njastad

This quantity generalizes the classical concept of orthogonal polynomials at the advanced unit circle or at the genuine line to orthogonal rational capabilities whose poles are between a prescribed set of advanced numbers. the 1st half treats the case the place those poles are all open air the unit disk or within the reduce part airplane. Classical issues reminiscent of recurrence kinfolk, numerical quadrature, interpolation homes, Favard theorems, convergence, asymptotics, and second difficulties are generalized and handled intimately. an identical themes are mentioned for a special scenario the place the poles can be found at the unit circle or at the prolonged actual line. within the final bankruptcy, numerous purposes are pointed out together with linear prediction, Pisarenko modeling, lossless inverse scattering, and community synthesis. This conception has many functions either in theoretical genuine and intricate research, approximation thought, numerical research, approach conception, and electric engineering.

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