Calculate the eigenfunctions of the spherical-cap concentration problem for a single angular order.

## Usage

`tapers`

, `eigenvalues`

= SHReturnTapersM (`theta0`

, `lmax`

, `m`

)

## Returns

`tapers`

: float, dimension (`lmax`

+1,`lmax`

+1)- The spherical harmonic coefficients of the
`lmax+1`

localization windows, arranged in columns. The first and last rows of each column correspond to spherical harmonic degrees 0 and`lmax`

, respectively, and the columns are arranged from best to worst concentrated. `eigenvalues`

: float, dimension (`lmax`

+1)- The concentration factors of the localization windows.

## Parameters

`theta0`

: float- The angular radius of the spherical cap in radians.
`lmax`

: integer- The spherical harmonic bandwidth of the localization windows.
`m`

: integer- The angular order of the localization windows.

## Description

`SHReturnTapersM`

will calculate the eigenfunctions (i.e., localization windows) of the spherical-cap concentration problem for a singular angular order. The spherical harmonic coefficients of each window are given in the columns of `tapers`

, and the corresponding concentration factors are given in `eigenvaules`

. The columns of `tapers`

are ordered from best to worst concentrated, and the first and last rows of each column correspond to spherical harmonic degrees 0 and `lmax`

, respectively. The localization windows are normalized such that they have unit power.

## References

Wieczorek, M. A. and F. J. Simons, Localized spectral analysis on the sphere,
`Geophys. J. Int.`

, 162, 655-675, 2005.

Simons, F.J., F.A. Dahlen, and M.A. Wieczorek, Spatiospectral concentration on a sphere, `SIAM Review`

, 48, 504-536, 2006.

## See also

shreturntapers, computedg82, computedm

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