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Converse to Taylor's Theorem and Beyond

Faculty Research Seminar

Speaker: Kevin Luli, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~kluli/
Location: 2112 MSB
Start time: Thu, Apr 18 2019, 1:00PM

Suppose at each point in a closed subset of R^n, we are given a degree m polynomial. How can we tell there exists an M-times continuously differentiable function F whose m-th degree Taylor polynomial agrees with the given polynomials and whose derivatives are controlled by the coefficients of the polynomials? Here M is an integer bigger than or equal to m. I will survey some known results and pose some related questions.