Mathematical Sciences: Studies in Approximation Theory and Orthogonal Polynomials

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The two investigators on this project will work on various problems in approximation theory and in the theory of orthogonal polynomials. Professor Nevai will concentrate on ordinary and generalized polynomial inequalities, difference and differential equations, spectral theory of tradiagonal and banded matrices, Toeplitz and Hankel forms, Hilbert space operators and Jacobi matrices. In addition to this analytical work Professor Nevai will continue to develop software for orthogonal polynomials. Professor Erdelyi will work on extremal properties of ordinary and generalized polynomials and on various types of polynomial inequalities that figure prominently in approximation theory. The investigators will work independently of each other on some problems and collaboratively on others, their talents complementing each other.