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linear algebra - Is taylor series also an orthogonal projection of a infinitely differentiable function on some subspace? - Mathematics Stack Exchange

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I'm wondering if there exists some inner product $\langle \cdot,\cdot \rangle$ defined on all real infinitely differentiable functions such that $$1, x, x^2, x^3, \ldots$$ are orthonormal w.r.t this

linear algebra - Is taylor series also an orthogonal projection of a infinitely differentiable function on some subspace? - Mathematics Stack Exchange Stack Internal Knowledge at work Bring the best of human thought and AI automation together at your work. Explore Stack Internal Is taylor series also an orthogonal projection of a infinitely differentiable function on some subspace? Ask Question Asked 3 years, 11 months ago Modified 2 years, 4 months ago Viewed 527 times 3 $\begingroup$ I'm wondering if there exists some inner product $\langle \cdot,\cdot \rangle$ defined on all real infinitely

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