Spectral theory of self-adjoint operators in Hilbert space
Spectral theory of self-adjoint operators in Hilbert space
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
On multivariate orthogonal polynomials
SIAM Journal on Mathematical Analysis
Orthogonality of analytic polynomials: a little step further
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
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Orthogonality of polynomials in several variables with respect to a positive Borel measure supported on an algebraic set is the main theme of this paper. As a step towards this goal quasi-orthogonality with respect to a non-zero Hermitian linear functional is studied in detail; this occupies a substantial part of the paper. Therefore necessary and sufficient conditions for quasi-orthogonality in terms of the three term recurrence relation modulo a polynomial ideal are accompanied with a thorough discussion. All this enables us to consider orthogonality in full generality. Consequently, a class of simple objects missing so far, like spheres, is included. This makes it important to search for results on existence of measures representing orthogonality on algebraic sets; a general approach to this problem fills up the three final sections.