FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 5, PAGES 85-90

**Estimates of sums of zero multiplicities for eigenfunctions of the
Laplace--Beltrami operator**

V. N. Karpushkin

Abstract

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We obtain an upper estimate $N$- c
(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 $$c
(M) is the Euler characteristic
of $M$.
There are given more strong estimates, but equivalent asymptotically
($N\; \to $¥), for the cases of
the sphere $S2$ and the
projective plane $$**R**^{2}.
Asymptotically more sharp estimate are shown for the case of
a domain on the plane.

Location: http://mech.math.msu.su/~fpm/eng/k05/k055/k05507h.htm

Last modified: February 26, 2006