On asymptotics of Lp extremal polynomials on a complex curve 0
Journal of Approximation Theory
Quantum information entropies and orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
Computation of the Entropy of Polynomials Orthogonal on an Interval
SIAM Journal on Scientific Computing
A Mathematical Theory of Communication
A Mathematical Theory of Communication
Shannon entropy of symmetric Pollaczek polynomials
Journal of Approximation Theory
Spreading lengths of Hermite polynomials
Journal of Computational and Applied Mathematics
Direct spreading measures of Laguerre polynomials
Journal of Computational and Applied Mathematics
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This is a brief account on some results and methods of the asymptotic theory dealing with the entropy of orthogonal polynomials for large degree. This study is motivated primarily by quantum mechanics, where the wave functions and the densities of the states of solvable quantum-mechanical systems are expressed by means of orthogonal polynomials. Moreover, the uncertainty principle, lying in the ground of quantum mechanics, is best formulated by means of position and momentum entropies. In this sense, the behavior for large values of the degree is intimately connected with the information characteristics of high energy states. But the entropy functionals and their behavior have an independent interest for the theory of orthogonal polynomials. We describe some results obtained in the last 15 years, as well as sketch the ideas behind their proofs.