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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

1992 • Question 5

Question

Math 6210 • Real Analysis 1992 • Question 5

In \(L^2((0,2\pi ))\) consider the orthogonal projection onto the subspace spanned by \(\{e^{-it},1,e^{it}\}\). Express this projection as an integral operator (i.e. an operator of the form \(f\to Pf\), where \(Pf(y)=\int _0^{2\pi }f(x)h(x,y)\,dx\)).

Raw LaTeX

In \(L^2((0,2\pi))\) consider the orthogonal projection onto the
subspace spanned by \(\{e^{-it},1,e^{it}\}\). Express this projection as an
integral operator (i.e. an operator of the form \(f\to Pf\), where
\(Pf(y)=\int_0^{2\pi}f(x)h(x,y)\,dx\)).

Topic Tags

Cauchy Integral Theory and Morera's Theorem Hilbert Spaces and Orthogonality Lebesgue Integration Lp Spaces and Sequence Spaces