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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1995 • Question 8

Question

Math 6420 • PDE Fall 1995 • Question 8
Find the spectral representation of the delta function for the selfadjoint operator \(L\) in the Hilbert space \(L^2(0,1)\) defined by \[ Lu=-u'',\quad\text{for }0\le x\le 1 \] \[ u(0)=0,\qquad\text{and}\qquad u(1)+u'(1)=0. \] **Part C** Do two of the four problems.

Raw LaTeX

Find the spectral representation of the delta function for the
selfadjoint operator \(L\) in the Hilbert space \(L^2(0,1)\) defined by
\[
  Lu=-u'',\quad\text{for }0\le x\le 1
\]
\[
  u(0)=0,\qquad\text{and}\qquad u(1)+u'(1)=0.
\]
\end{enumerate}

\examheading{Part C}

Do two of the four problems.

\begin{enumerate}

Topic Tags

Adjoint Operators and Riesz Representation Distributions and Weak Solutions Fundamental Solutions Spectral Theory of Operators