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math.FA2026
Methods of Construction of Exponential Bases on Planar Domains Revised
Oleg Asipchuk, Laura De Carli
In [1], we surveyed classical and recent results on the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We also construc…
math.NT2026
Cyclotomy of symmetric polynomials
Laura De Carli, Maurizio Laporta
We prove some new identities for homogeneous symmetric polynomials when evaluated at roots of unity. Some of these formulas are applied to obtain new insights onto cyclotomic polyn…
math.FA2026
Block-equivalent finite Gabor frames
Oleg Asipchuk, Laura De Carli, Luis Rodriguez
We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal mat…