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Ball Prolate Spheroidal Wave Functions In Arbitrary Dimensions. (arXiv:1802.03684v1 [math.NA])
来源于:arXiv
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of
real order $\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball
PSWFs. They are eigenfunctions of both a weighted concentration integral
operator, and a Sturm-Liouville differential operator. Different from existing
works on multi-dimensional PSWFs, the ball PSWFs are defined as a
generalisation of orthogonal {\em ball polynomials} in primitive variables with
a tuning parameter $c>0$, through a "perturbation" of the Sturm-Liouville
equation of the ball polynomials. From this perspective, we can explore some
interesting intrinsic connections between the ball PSWFs and the finite Fourier
and Hankel transforms. We provide an efficient and accurate algorithm for
computing the ball PSWFs and the associated eigenvalues, and present various
numerical results to illustrate the efficiency of the method. Under this
uniform framework, we can recover the existing PSWFs by suitable variable
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