Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Shafkulovska, Irina"'
Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution. We investigate the question which metaplectic Wigner d
Externí odkaz:
http://arxiv.org/abs/2405.12112
We study Gabor frames with Hermite window functions. Gr\"ochenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the ``safety region". For rectangular lattices and Hermite windows of order 4 an
Externí odkaz:
http://arxiv.org/abs/2403.10503
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive samples. These co
Externí odkaz:
http://arxiv.org/abs/2311.08352
Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural" classes of periodic configurations. Also, we rule out the option tha
Externí odkaz:
http://arxiv.org/abs/2306.16266
Publikováno v:
Proceedings of the American Mathematical Society, Series B. 12/17/2024, Vol. 11, p664-679. 16p.
Autor:
Führ, Hartmut, Shafkulovska, Irina
We study the mapping properties of metaplectic operators $\widehat{S}\in \mathrm{Mp}(2d,\mathbb{R})$ on modulation spaces of the type $\mathrm{M}^{p,q}_m(\mathbb{R}^d)$. Our main result is a full characterisation of the pairs $(\widehat{S},\mathrm{M}
Externí odkaz:
http://arxiv.org/abs/2211.08389
This article bridges and contributes to two important research areas, namely the completeness problem for systems of translates in function spaces and the short-time Fourier transform (STFT) phase retrieval problem. As a first main contribution, we s
Externí odkaz:
http://arxiv.org/abs/2211.05687
We study the spectral bounds of self-adjoint operators on the Hilbert space of square-integrable functions, arising from the representation theory of the Heisenberg group. Interestingly, starting either with the von Neumann lattice or the hexagonal l
Externí odkaz:
http://arxiv.org/abs/2209.04202
Autor:
Faulhuber, Markus, Shafkulovska, Irina
We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the frame boun
Externí odkaz:
http://arxiv.org/abs/2204.02917
Publikováno v:
In Journal of Approximation Theory March 2025 306