Average Growth of the Spectral Function on a Riemannian Manifold

TY - JOUR

T1 - Average Growth of the Spectral Function on a Riemannian Manifold

AU - Lapointe, Hugues

AU - Polterovich, Iosif

AU - Safarov, Yuri

PY - 2009/6

Y1 - 2009/6

N2 - We study average growth of the spectral function of the Laplacian on a Riemannian manifold. Two types of averaging are considered: with respect to the spectral parameter and with respect to a point on a manifold. We obtain as well related estimates of the growth of the pointwise -function along vertical lines in the complex plane. Some examples and open problems regarding almost periodic properties of the spectral function are also discussed.

AB - We study average growth of the spectral function of the Laplacian on a Riemannian manifold. Two types of averaging are considered: with respect to the spectral parameter and with respect to a point on a manifold. We obtain as well related estimates of the growth of the pointwise -function along vertical lines in the complex plane. Some examples and open problems regarding almost periodic properties of the spectral function are also discussed.

U2 - 10.1080/03605300802537453

DO - 10.1080/03605300802537453

M3 - Article

VL - 34

SP - 581

EP - 615

JO - COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

JF - COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

IS - 6

ER -