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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1994 • Question 9

Question

Math 6420 • PDE Fall 1994 • Question 9

Find the spectral representation of the delta function for the operator \(L\) defined by \(Lu=-u''\) on \(x\in (-\infty ,0]\) with boundary condition \(u(0)=0\). Then solve the problem \(Lu=f\) if \(f(x)=1\) for \(-2\le x\le -1\) and \(f(x)=0\) elsewhere.

Raw LaTeX

Find the spectral representation of the delta function for the
operator \(L\) defined by \(Lu=-u''\) on \(x\in(-\infty,0]\) with boundary condition \(u(0)=0\).
Then solve the problem \(Lu=f\) if \(f(x)=1\) for \(-2\le x\le -1\) and \(f(x)=0\) elsewhere.

Topic Tags

Distributions and Weak Solutions Fundamental Solutions Linear Programming and Optimization Spectral Theory of Operators