**June 09, 2016 at 09:00 - June 24, 2016**
- BCAM

**Sébastien BRETEAUX, BCAM**

DATES: 9 June (9:00 - 11:00), 10 June (10:00 - 12:00), 23 & 24 June (9:30 - 11:30). A total of 8 hours.

The spectral theorem is one of the most important theorems of linear algebra: it tells us that any Hermitian matrix H can be diagonalized in an orthonormal basis.

As a corollary one can (when it makes sense) define functions of the matrix H, like its square root, its inverse, its exponential, etc., by applying the function to the coefficients of the diagonal matrix.

For many applications, the framework of matrices is to restrictive. For example, in mathematical physics, it is very common to consider self-adjoint operators in a Hilbert space.

In this course, we will see how this theorem generalizes to operators on a Hilbert space, and how one then deduces a functional calculus for such operators.

REFERENCES

[1] Pierre Lévy-Bruhl, Introduction à la théorie spectrale

[2] Riesz, Nagy, Functional Analysis

[3] Rudin, Functional Analysis

[4] Reed, Functional Analysis, (Simon, Methods of mathematical physics, vol. 1)

***Registration is free, but inscription is required before 7th June: **So as to inscribe send an e-mail to

roldan@bcamath.org. Student grants are available. Please, let us know if you need support for travel and accommodation expenses.