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math.CA2024
Estimates for strongly singular operators along curves
Magali Folch-Gabayet, Ricardo A. Sáenz
For a proper function on the plane, we study the operator \[ Tf(x,y) = \lim_{\varepsilon\to 0} \int_\varepsilon^1 f(x-t,y-t^k) \frac{e^{2πi γ(t)}}{ψ(t)} dt, \] where an…
math-ph2024
Lower and upper bounds for configurations of points on a sphere
Paolo Amore, Ricardo A. Sáenz
We present a new proof (based on spectral decomposition) of a bound originally proved by Sidelnikov~\, for the frame potentials $\sum_{ij} \left( {\bf P}_i \cdot {\bf P}_j \right)^…