Author

R. Zarouf

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Preprint Aug 2026

Sch\"affer's matrix inequality: the exact asymptotic constant

Let $S_n$ denote the smallest constant such that \[ |\det T|\|T^{-1}\| \leq S_n \|T\|^{n-1} \] for every invertible operator $T$ on every $n$-dimensional complex Banach space. In Hilbert space the optimal constant is $1$. For arbitrary Banach spaces, J. J. Sch\"affer proved in 1970 that \[S_n\leq \sqrt{en}. \] Subseque...

Samy Houache, O. Szehr, R. Zarouf · 0 citations

Preprint Jul 2026

Projected Inner-Function Dynamics and Crystalline Measures of Meyer-Blaschke type

We generalize a construction of Yves Meyer of sparse crystalline measures arising from powers of a Blaschke factor. Starting from a recursion $f_n=\theta^n f_0$ on the unit circle where $\theta$ is an inner function, we project the Fourier coefficient array $\widehat{f_n}(k)$ to the real line by placing its entries at...

O. Szehr, R. Zarouf · 0 citations