# Analysis Group

With the support of the National Science Foundation, our group organizes the annual New Mexico Analysis Seminar jointly with analysts from the University of New Mexico.

### Faculty Interest

#### Jameson Cahill

Applied Harmonic Analysis

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Xuemei Chen

Applied Harmonic Analysis, Sparse Signal Recovery: compressed sensing, frame theory, and fast linear solvers for high dimensional data

#### Dante De Blassie

Probability: Brownian motion, reflected Brownian motion and conditioned Brownian motion; stochastic differential equations and diffusion processes; symmetric stable processes; exit times.

#### Tiziana Giorgi

Nonlinear Partial Differential Equations, Calculus of Variation

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Andres Contreras Marcillo

Calculus of Variation, Nonlinear Analysis

#### Joseph Lakey

Harmonic Analysis: time-frequency analysis, wavelets, information theory and applications to signal processing, discrete dynamical systems.

#### Robert Smits

Stochastic and Harmonic Analysis: stochastic differential equations, spectral theory, asymptotic analysis, heat kernels, large deviations, mathematical finance, eigenvalue estimates.

#### Christopher Stuart

Functional Analysis: uniform boundedness principles, barrelled spaces, the topological vector space properties of sequence spaces.

### Emeritus Faculty

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Dick Bagby

Real and Harmonic Analysis: Classical analysis in Euclidean space. Convolution and Fourier multipliers. Continuity properties of operators and bounds for maximal functions in terms of function space norms. Questions of pointwise convergence.

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Chuck Swartz

Functional Analysis: topological vector spaces, infinite matrices and gliding hump properties in sequence and function spaces, vector and operator valued series, vector-valued measures, and integrals.

#### Doug Kurtz

Harmonic Analysis: maximal functions, singular integrals, multipliers, Littlewood-Paley operators, weighted norm inequalities.