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Fix typo
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Hadrien-Montanelli committed Dec 4, 2023
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Expand Up @@ -341,7 +341,7 @@ <h4>Results (Postdoc at Columbia)</h4>
<img src="/blog/nonlocalpdesphere.jpg" class="img-responsive">
</center>

<p>Several years later, in 2023, I introduced a nonlocal vector calculus on the sphere based on weakly singular integral operators. When employing scalar and vector spherical harmonics as bases, I showed that our nonlocal operators exhibit diagonal behavior. Through analysis, I also established strong convergence to the operators of local vector calculus as the interaction range approaches zero. This work is consistent with my previous work on nonlocal diffusion operators. This extends to the sphere, a prototype of a manifold, the nonlocal calculus for Euclidean domains.</p>
<p>Several years later, in 2023, I introduced a nonlocal vector calculus on the sphere based on weakly singular integral operators. When employing scalar and vector spherical harmonics as bases, I showed that these nonlocal operators exhibit diagonal behavior. Through analysis, I also established strong convergence to the operators of local vector calculus as the interaction range approaches zero. This work is consistent with my previous work on nonlocal diffusion operators. This extends to the sphere, a prototype of a manifold, the nonlocal calculus for Euclidean domains.</p>

<h4>Collaborators</h4>

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