How Fast Do Polynomials Grow on Semialgebraic Sets ?

  title={How Fast Do Polynomials Grow on Semialgebraic Sets ?},
  author={Pinaki Mondal and Tim Netzer},
We study the growth of polynomials on semialgebraic sets. For this purpose we associate a graded algebra to the set, and address all kinds of questions about finite generation. We show that for a certain class of sets, the algebra is finitely generated. This implies that the total degree of a polynomial determines its growth on the set, at least modulo bounded polynomials. We however also provide several counterexamples, where there is no connection between total degree and growth. In the plane… CONTINUE READING

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