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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2007 • Question 9

Question

Math 6410 • ODE Fall 2007 • Question 9

Characterize the orthogonal complement of \(H_0^1(a,b)\) in the space \(H^1(a,b)\), where \((a,b)\) is a real interval which is either finite or else \(b=\infty \) or else \(a=-\infty \), \(b=\infty \).

Raw LaTeX

Characterize the orthogonal complement of \(H_0^1(a,b)\) in the space \(H^1(a,b)\),
where \((a,b)\) is a real interval which is either finite or else \(b=\infty\) or else
\(a=-\infty\), \(b=\infty\).

Topic Tags

Hilbert Spaces and Orthogonality Sobolev Spaces and Energy Estimates