HATA. DTU Compute

Research group · DTU Mathematics

Finding structure
in signals
and spaces.

We are HATA — Harmonic Analysis, Theory and Application, a research group at DTU Compute. We study how complex functions and signals can be understood through elegant, stable mathematical representations.

Explore our research See recent papers

Fundamental mathematics. Structured representations. Real-world connections.

FRAME THEORY TIME-FREQUENCY ANALYSIS WAVELETS & SHEARLETS OPERATOR THEORY MATHEMATICS OF ML AND AI

01 / WHAT WE DO

The ideas behind
the analysis.

Frame theory is at the heart of our work. From abstract Hilbert spaces to practical signal representations, we explore the mathematics of decomposing, reconstructing and understanding information.

01 /

Frame theory & duality

Redundant expansions, stability, dual frames and frame constructions in finite- and infinite-dimensional spaces.

HILBERT SPACES · RECONSTRUCTION
02 /

Time-frequency analysis

Gabor systems, localization and the mathematical interplay of time and frequency in structured representations.

GABOR FRAMES · FOURIER METHODS
03 /

Wavelets & multiscale methods

Wavelets, shearlets and generalized shift-invariant systems for structure across scales and directions.

SCALE · GEOMETRY · DIRECTION
04 /

Operators & applications

Operator orbits, dynamical sampling and connections to approximation, inverse problems and signal processing.

SAMPLING · APPLIED ANALYSIS
05 /

Mathematics of Machine Learning & AI

Mathematical foundations and theory of ML and AI, their applications, and their use in mathematics teaching.

APPLICATIONS · THEORY · TEACHING

IN FOCUS / FROM OUR PAPERS

Mathematics, pictured.

The intricate geometry of the obstructions to the Gabor frame property for B-splines is surprisingly complex. The hyperbolic slits in the parameter plane reveal just how subtle the frame-set boundary can be.

Read the paper on arXiv
A mathematical parameter plot with two wedge-shaped regions near b equals 200 and 201, small coloured segments indicating the product ab, and dashed hyperbolic boundaries.
FIG. 02 / From A new family of hyperbolic slits in the Gabor frame set of B-spline generators · Jakob Lemvig (2026)

02 / RECENTLY AT HATA

Recently, at HATA.

Research, publications and occasional news from the group.

SOURCED FROM arXiv + DTU ORBIT · AUTOMATED

LATEST PAPERS

  1. arXiv PREPRINT · math.FA

    The zero set of the Zak transform of B-splines with applications to Gabor frames

    Marzieh Hasannasab, Jakob Lemvig

    arXiv

  2. arXiv PREPRINT · math.CA

    Directional polynomial frames on spheres

    Marzieh Hasannasab, Larissa Kaldewey, Frederic Schoppert

    arXiv

  3. arXiv PREPRINT · math.FA

    A new family of hyperbolic slits in the Gabor frame set of B-spline generators

    Jakob Lemvig

    arXiv

  4. DTU ORBIT PUBLICATION

    Two results on polynomially-generated wavelet frames and nonorthogonal polynomial frames

    Ole Christensen, Hong Oh Kim, Rae Young Kim

    Orbit

  5. arXiv PREPRINT · ORBIT RECORD

    Weaving Information Packets

    Ole Christensen, Hong Oh Kim, Rae Young Kim

    Orbit arXiv

OTHER NEWS

  1. PHD DEFENCE · NTNU

    Marzieh Hasannasab served on the PhD defence committee at NTNU

    On 3 September 2026, Marzieh Hasannasab served as a member of the PhD defence committee for Erling Arnold Tønseth Svela’s thesis, Quantum harmonic and time-frequency methods for concentration problems in phase space, at NTNU.

    NTNU researcher page

PUBLICATION DIRECTORIES

Looking for a
particular paper?

Search HATA publications directly in arXiv and DTU Orbit. Orbit's combined search can miss records, so the researcher profiles below remain the most complete Orbit route.

DTU OrbitCombined HATA publication search arXivHATA author search · newest first

03 / THE PEOPLE

Three researchers.
One research group.

The group brings together different perspectives on harmonic analysis, structured function systems and their connections to applied mathematics.

MH03 / 03

Assistant Professor · Tenure Track

Marzieh
Hasannasab

Gabor analysis · dynamical sampling · operator theory · structured frames · mathematics of ML & AI

Profile Orbit publications Email

ABOUT THE GROUP

Mathematics at the heart
of modern signal analysis.

HATA was founded in 2014 and is part of the Section for Mathematics at DTU Compute, Technical University of Denmark.

We welcome conversations about harmonic analysis, mathematical collaborations and research opportunities.

Explore Mathematics at DTU