# Analysis

The research activities of the **Analysis group** are divided into four focus areas:

**Complex Analysis** is a powerful tool in engineering, for example in hydrodynamics, signal analysis and control theory, and theoretical physics. These applications again lead to exciting new problems in complex analysis.

**Harmonic Analysis** develops a signal into a collection of pure waves (harmonics), and then use this development to analyze the signal, including its compression and transmission.

**Noncommutative Geometry** extends the natural correspondence between geometric spaces and commutative algebras to the noncommutative case. This allows us to extend the classical tools—such as measure theory, topology, differential calculus and Riemannian geometry—to the noncommutative situation.

**Arithmetical Physics** has become a vast area, which, among many other things, explores the possibility of describing phenomena below the Planck length by using fields and rings other than the usual real and complex numbers.

## Contact

### Upcoming Events

## Current Projects

- Quantum Metric and Semiclassical Aspects of Time-Frequency Analysis
**Peder Sather Grant 2015**

Project leaders: Franz Luef, Maciej Zworski

Team members: Yura Lyubarskii, Eugenia Malinnikova, Marc A. Rieffel, Isaac A. Romero- Dirichlet Series and Analysis on Polydiscs (DISPDISC) (NFR, 2013‑2018)
- Discrete Models in Mathematical Analysis (DiMMA) (NFR, 2012‑2016)

## Seminars and Conferences

## Recent Publications

Frederic Bayart, Herve Queffelec and Kristian Seip

**Approximation numbers of composition operators on H^p spaces of Dirichlet series**

*Annales de l'Institut Fourier*

Andrii Bondarenko and Kristian Seip

**Helson's problem for sums of a random multiplicative function**

*Mathematika*

Andrii Bondarenko, Titus Hilberdink and Kristian Seip

**Gal-type GCD sums beyond the critical line**

*Journal of Number Theory*

Ole Fredrik Brevig

**Zeros of functions in Bergman-type Hilbert spaces of Dirichlet series**

*Mathematica Scandinavica*

Ole Fredrik Brevig and Maxime Bailleul

**Composition operators on Bohr-Bergman spaces of Dirichlet series**

*Annales Academiae Scientiarum Fennicae Mathematica*

Ole Fredrik Brevig

**An embedding constant for the Hardy space of Dirichlet series**

*Proceedings of the American Mathematical Society*

Ole Fredrik Brevig, Karl-Mikael Perfekt, Kristian Seip, Aristomenis Siskakis and Dragan Vukotic

**The multiplicative Hilbert matrix**

*Advances in Mathematics*

Magnus B. Landstad, Steve Kaliszewski and John Quigg

**Exotic Coactions**

*Proceedings of the Edinburgh Mathematical Society*