2025/11/14 by David G. Costa, Costa, David G., Hossein Tehrani +1
Mathematics · #Advanced Combinatorial Mathematics #Holomorphic and Operator Theory #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.2511.11904
After a brief review of the definition of the Trudinger-Moser functions in dimension N=2 and some basic notions in the theory of ``Reproducing Kernel Hilbert Spaces (RKHS)'', we will show that there is a close connection between those two topics. More precisely, among other things, we start by considering a properly chosen multiple of the classical Trudinger-Moser family of functions in dimension N=2, which we denote by γt (r) := (1)/(2π)min \ log (1)/(r), log (1)/(t) \ , where 0 < t , r < 1, and using the theory of RKHS we will show that γt can be seen as a ``bounded'' (linear) evaluation functional u \longrightarrow u(t) for functions u in a suitable Hilbert Space \cal H. A slightly different definition for a ''Trudinger-Moser'' type function will also be considered for N≥ 3.