5 papers
Projected Inner-Function Dynamics and Crystalline Measures of Meyer-Blaschke type
Oleg Szehr, Rachid Zarouf
We generalize a construction of Yves Meyer of sparse crystalline measures arising from powers of a Blaschke factor. Starting from a recursion on the unit circle wher…
Lower bounds in -rational approximation to Blaschke products
Laurent Baratchart, Alexander Borichev, Sylvain Chevillard +2
We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space of the unit disk. We first consider approximation to $z^…
Asymptotic sharpness of a Nikolskii type inequality for rational functions in the Wiener algebra
Benjamin Auxemery, Alexander Borichev, Rachid Zarouf
We establish the asymptotic sharpness of a Nikolskii type inequality proved by A. Baranov and R. Zarouf for rational functions in the Wiener algebra of absolutely convergent Fo…
On the Exact Maxwell evolution equation of resonator dynamics
Tong Wu, Rachid Zarouf, Philippe Lalanne
In a recent publication [Opt. Express 32, 20904 (2024)], the accuracy of the main evolution equation that governs resonator dynamics in the coupled-mode theory (CMT) was questioned…
Bernstein-type inequalities for mean -valent functions
Anton Baranov, Ilgiz Kayumov, Rachid Zarouf
We derive new integral estimates of the derivatives of mean -valent functions in the unit disk. Our results develop and complement estimates obtained by E.P. Dolzhenko and A.A.…