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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1997 • Question 8

Question

Math 6420 • PDE Fall 1997 • Question 8
Find the spectral representation of the delta function for the operator \[ Lu=-\frac{d^2u}{dx^2},\qquad x\in[0,\infty),\qquad u(0)=u'(0). \] Classify the spectrum of this operator. **Applied Math Qualifying Exam Part C** Do two out of the four problems for full credit on Part C.

Raw LaTeX

Find the spectral representation of the delta function for the
operator
\[
  Lu=-\frac{d^2u}{dx^2},\qquad x\in[0,\infty),\qquad u(0)=u'(0).
\]
Classify the spectrum of this operator.
\end{enumerate}

\examheading{Applied Math Qualifying Exam Part C}

Do two out of the four problems for full credit on Part C.

\begin{enumerate}

Topic Tags

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