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Fundam. Prikl. Mat., 2005, Volume 11, Issue 5, Pages 85–90 (Mi fpm867)  

Estimates of sums of zero multiplicities for eigenfunctions of the Laplace–Beltrami operator

V. N. Karpushkin

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We obtain an upper estimate $N-\chi(M)$ for the sum $Q_N$ of singular zero multiplicities of the $N$th eigenfunction of the Laplace–Beltrami operator on the two-dimensional, compact, connected Riemann manifold $M$, where $\chi(M)$ is the Euler characteristic of $M$. There are given more strong estimates, but equivalent asymptotically ($N\to\infty$), for the cases of the sphere $S^2$ and the projective plane $\mathbb R^2$. Asymptotically more sharp estimate are shown for the case of a domain on the plane.

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English version:
Journal of Mathematical Sciences (New York), 2007, 146:1, 5509–5512

Bibliographic databases:

UDC: 517.586

Citation: V. N. Karpushkin, “Estimates of sums of zero multiplicities for eigenfunctions of the Laplace–Beltrami operator”, Fundam. Prikl. Mat., 11:5 (2005), 85–90; J. Math. Sci., 146:1 (2007), 5509–5512

Citation in format AMSBIB
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\by V.~N.~Karpushkin
\paper Estimates of sums of zero multiplicities for eigenfunctions of the Laplace--Beltrami operator
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 5
\pages 85--90
\mathnet{http://mi.mathnet.ru/fpm867}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2216854}
\zmath{https://zbmath.org/?q=an:1149.58011}
\elib{http://elibrary.ru/item.asp?id=9127602}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 146
\issue 1
\pages 5509--5512
\crossref{https://doi.org/10.1007/s10958-007-0363-3}
\elib{http://elibrary.ru/item.asp?id=13535628}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548809793}


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  • Фундаментальная и прикладная математика
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