A polynomial on Rn is a function of the form where the aj1, j n 's are scalars and N1, ,Nn N Prove that if A is compact in Rn and f C(A), then there is a sequence of polynomials Pk on Rn such that Pk f uniformly on A as k Ni Nu

Question: A polynomial on Rn is a function of the form where the aj1,. . . . . .. j n 's are scalars and N1,...,Nn

A polynomial on Rn is a function of the form

where the aj1,. . . . . .. j n 's are scalars and N1,...,Nn ˆˆ N. Prove that if A is compact in Rn and f ˆˆ C(A), then there is a sequence of polynomials Pk on Rn such that Pk †’ f uniformly on A as k: †’ ˆž.

Ni Nu

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