Research Interests

My research interests include: time-frequency analysis, abstract harmonic analysis, operator algebras, noncommutative geometry, frame theory, and quantum harmonic analysis. My PhD work focused on exploiting the localization of imprimitivity bimodules to extract and extend results in Gabor analysis. This includes the extension of Gabor-stability property to the Heisenberg modules and a topological characterization of lattice invariant (translation and modulation) operators in quantum harmonic analysis.

I am also engaged in the theory of frames, which is a foundational tool in the study of non-orthogonal expansions in functional analysis.

Publications and Preprints

Publications

Arvin Lamando and Henry McNulty. “On Modulation and Translation Invariant Operators and the Heisenberg Module.” In: J. Fourier Anal. Appl. 31.4 (2025), Paper No. 56, 43. url: https://doi.org/10.1007/s00041-025-10176-5.
Malte Gerhold, Arvin Lamando, and Franz Luef. “Linear Deformations of Heisenberg Modules and Gabor Frames.” In: Journal of Mathematical Analysis and Applications (2026), p.130540. url:https://www.sciencedirect.com/science/article/pii/S0022247X26001526.

Proceedings

Arvin Lamando and Gino Angelo Velasco. “Adaptive Frames from Quilted Local Time-Frequency Systems”. In: 2019 13th International conference on Sampling Theory and Applications (SampTA). 2019, pp. 1–4. doi: 10.1109/SampTA45681.2019.9030819.

PhD Dissertation

Operator Quantization and Deformation on the Heisenberg Modules.

MS Thesis

Adaptive Frames from Local Time-Frequency Systems.

Ongoing Projects

Generalized Continuous-Trace C*-Algebras via Hilbert C*-Modules and Module Frame Theory (with Stefan Wagner)
Computing non-Abelian Groupoid Cohomology (with Nata Machado and Stefan Wagner)
Tensor Products and Frame Theory on Hilbert C*-Modules (with Dimitri Bytchenkoff and Franz Luef)
On Fourier Standard Spaces (with Hans Feichtinger and Lenny Neyt)

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