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Functional Analysis


Continuation of Math 960.


Functional Analysis, Buhler, American Mathematical Society, 2018.

Credit Hours: 

The general theme of the course is the spectrum of operators on Hilbert space, with an emphasis on explicit calculation of spectra (and of spectrally related things like traces, when appropriate). After a review of essential information about Hilbert space and bounded operators on Hilbert space, we will treat compact operators, especially the selfadjoint ones. Many interesting examples of compact operators with more or less computable spectrum and trace come from inverting unbounded operators associated to ODE and PDE problems, so we will have a look at unbounded operators. The situation of operators with entirely continuous spectrum will be represented by the calculation of the spectrum of the combinatorial Laplacian of a homogeneous tree, and by other examples from infinite combinatorics and elsewhere as time permits.

(Stefanov 2020 )

Events Calendar

Using Math

CTE course transformation grant helps Emily Witt, assistant professor of math, develop active learning with student groups in calculus.  Positive results using modules developed with Justin Lyle and Amanda Wilkens, math graduate students, were attained.  Read more

Math and COVID-19: Sources on how math is being used to track the virus and its spread.  AMS link.

A mathematician-musician's breakthrough melds East, West. Read more.

Researcher's innovative approach to flood mapping support emergency management and water officials. Read more.

Nicole Johnson found a way to express her baton twirling using math. See video.