We consider the Laplace operator on the finite-dimensional linear space of algebraic polynomials in N variables such that each variable occurs at most with the power n. The space of the polynomials is equipped with the Laguerre norm. We establish safe lower and upper bounds for the norm of the Laplace operator on this space, and we derive asymptotic lower and upper bounds for this norm as n goes to infinity. The asymptotic bounds are better than the safe bounds.
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