Mother Bodies

Gustafsson, B; Putinar, M

doi:10.1007/978-3-319-65810-0_6

Mother Bodies

Lookup NU author(s): Professor Mihai Putinar

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Abstract

© Springer International Publishing AG 2017. We outline the general theory for a certain kind of potential theoretic skeletons, or ‘mother bodies’, associated to a given domain. The hope is, generally speaking, that such skeletons can be identified as attractors for zeros of orthogonal polynomials, and in a few cases such expectations have indeed been met, theoretically and/or experimentally. For the exponential polynomials the success is rather limited so far, but by building in enough flexibility in the models one expects in some not so distant future to reach a reasonable matching. In the present chapter we set up desirable properties (formulated as ‘axioms’) to be satisfied by mother bodies. Since the search for potential theoretic skeletons is a highly ill-posed problem (related to the Cauchy problem for an elliptic operator) very few domains admit mother bodies, but for domains with piecewise algebraic boundaries there is a rather constructive and efficient theory, bearing in mind that the same class of domains is also amenable for studying zeros of orthogonal polynomials.