Some remarks on spherical harmonics

Details Some remarks on spherical harmonics Some remarks on spherical harmonics

2007-05-17

arxiv.org/abs/0705.2547v3

Algebra i Analiz, 2008, V. 20, No 4, 64--86 (in Russian)

Mathematics

Classical Analysis and ODEs

20 pages. Translation of the version which is published in Russian. Minor modifications throughout the paper. An error in calc

Scientific paper

The article contains several observations on spherical harmonics and their nodal sets: a construction for harmonics with prescribed zeroes; a kind of canonical representation of this type for harmonics on $\bbS^2$; upper and lower bounds for nodal length and inner radius (the upper bounds are sharp); precise upper bound for the number of common zeroes of two spherical harmonics on $\bbS^2$; the mean Hausdorff measure on the intersection of $k$ nodal sets for harmonics of different degrees on $\bbS^m$, where $k\leq m$ (in particular, the mean number of common zeroes of $m$ harmonics).

Affiliated with

Also associated with

No associations

Rating

Some remarks on spherical harmonics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some remarks on spherical harmonics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some remarks on spherical harmonics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-142497