Bounds for the Bergman Kernel and the Sup-Norm of Holomorphic Siegel Cusp Forms
Sign Up to like & getrecommendations! Published in 2024 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnad322
Abstract: We prove “polynomial in $k$” bounds on the size of the Bergman kernel for the space of holomorphic Siegel cusp forms of degree $n$ and weight $k$. When $n=1,2$ our bounds agree with the conjectural… read more here.
Keywords: holomorphic siegel; cusp forms; bergman kernel; siegel cusp ... See more keywords
Relative Stability in the Sup-Norm and Input-to-State Stability in the Spatial Sup-Norm for Parabolic PDEs
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Automatic Control"
DOI: 10.1109/tac.2022.3192325
Abstract: In this article, we introduce the notion of relative $\mathcal {K}$-equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturbances for nonlinear parabolic partial differential equations (PDEs). Based on the RKES,… read more here.
Keywords: stability; parabolic pdes; sup norm; spatial sup ... See more keywords
Optimal sup norm bounds for newforms on GL2 with maximally ramified central character
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DOI: 10.1515/forum-2020-0080
Abstract: Abstract Recently, the problem of bounding the sup norms of L2{L^{2}}-normalized cuspidal automorphic newforms ϕ on GL2{\mathrm{GL}_{2}} in the level aspect has received much attention. However at the moment strong upper bounds are only available… read more here.
Keywords: sup norm; newforms gl2; norm bounds; sup ... See more keywords