| Abstract: |
| \begin{abstract}
I will present results obtained jointly with R. Schilling (Dresden) and P. Sztonyk (Wroclaw) on the spatial decay of resolvent kernels for a broad class of non-local L\`evy operators, as well as on eigenfunctions of the associated Schr\odinger operators [B]. Our results lead to general theorems concerning L\`evy measures with exponential and subexponential decay at infinity. In particular, we identify sharp qualitative transitions in these decay properties, thereby extending classical results of Carmona, Masters, and Simon [A] for the fractional Laplacian (subexponential decay) and relativistic operators (exponential decay). Moreover, these transitions in eigenfunction decay admit a natural energetic interpretation, which will also be discussed during the talk.
References:
[A] R. Carmona, W. C. Masters, and B. Simon, Relativistic Schr\odinger operators: asymptotic
behavior of the eigenfunctions, J. Funct. Anal. 91(1) 117--142 (1990)
[B] K. Kaleta, R.L. Schilling, P. Sztonyk, Decay of resolvent kernels and Schr\odinger eigenstates
for L\`evy operators, Math. Ann. 394(4), 88 (2026)
\end{abstract} |
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