caa a22 4500 388109076 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500013172 doi S0308210500013172 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500013172 Asymptotics for the spectral heat function and bounds for integrals of Dirichlet eigenfunctions [Elektronische Daten] We introduce the spectral heat function H associated with the Dirichlet-Laplace-Beltrami operator ΔM on a compact smooth Riemannian manifold M with a non-empty smooth boundary. We obtain two-term asymptotics for H without assuming any billiard conditions on M. As a corollary, we obtain estimates for the integral of the k′th Dirichlet eigenfunction of ΔM over M for k→∞. Copyright © Royal Society of Edinburgh 1999 van den Berg M. School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK Watson S. P. School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 841-854 0308-2105 129:4<841 1999 129 PRM https://doi.org/10.1017/S0308210500013172 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500013172 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- van den Berg M. School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK NATIONALLICENCE 700 1- Watson S. P. School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 841-854 0308-2105 129:4<841 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge