منابع مشابه
Generalized Prolate Spheroidal Functions
Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications, GPSFs are often replaced by crude approximations. The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues. This pape...
متن کاملNew investigation for the spheroidal wave functions ∗
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions’ eigenvalue problem. Expanded by the parameter α, the first order term of ground eigen-value and the eigen-function are gotten. In virtue of the good form of the first term in the superpotential and its shape-invariant property in the first order, we also obtain the eigenvalues an...
متن کاملGeneralized and Fractional Prolate Spheroidal Wave Functions
An important problem in communication engineering is the energy concentration problem, that is the problem of finding a signal bandlimited to [−σ, σ] with maximum energy concentration in the interval [−τ, τ ], 0 < τ, in the time domain, or equivalently, finding a signal that is time limited to the interval [−τ, τ ] with maximum energy concentration in [−σ, σ] in the frequency domain. This probl...
متن کاملSolve spheroidal wave functions by SUSY method ∗
In the paper, we study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics (SUSYQM). For the ground state, the first three terms of ground eigenvalue and eigenfunction in parameter α = aw are obtained. The obtained ground eigenfunction is elegantly in closed forms. Due to th...
متن کاملChromatic Series and Prolate Spheroidal Wave Functions
The Ignjatovic theory of chromatic derivatives and series is extended to include other series. In particular series of prolate spheroidal wave functions are used to replace the orthogonal polynomial series in this theory. It is extended further to prolate spheroidal wavelet series that enables us to combine chromatic series with sampling series.
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences
سال: 1970
ISSN: 0098-8979
DOI: 10.6028/jres.074b.018