Read, highlight, and take notes, across web, tablet, and phone. Slepian functions, numerical evaluation of prolate spheroidal wave functions. Properties of the functions are derived and several applications to the representation of. Schrodinger equation, positiondependent mass, quadratic lienard type oscillator equation, prolate spheroidal wave function. The magic of the prolate spheroidal functions in various. This option allows users to search by publication, volume and page selecting this option will search the current publication in context.
Topics include separation of the scalar wave equation in spheroidal coordinates, angle and radial functions, integral representations and relations, and expansions in spherical bessel function products. Theory and computation of the spheroidal wave functions. These functions are studied in the paleywiener space flammer, 2014. Prolate spheroidal wave functions and their properties computation of the pswfs by flammers method uniform estimates of the pswfs and their derivatives applications of the pswfs cimpa school on real and complex analysis with applications, buea cameroun, 114 may 2011. New relations are found between the spheroidal and spherical wave functions, as well as between the spheroidal functions related to different spheroidal coordinate systems. The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics. Pdf theory and computation of spheroidal wavefunctions. A new integral equation for the spheroidal equations in. Calculating the branch points of the eigenvalues of the coulomb. Computational geometric and boundary value properties of. A set of tables of spheroidal wave functions designed to simplify the computation of acoustic and electromagnetic scattering from spheroids. Sound radiation from point acoustic sources with shield of. Prolate spheroidal wave functions pswfs are the eigenfunctions of the bandlimited operator in one dimension. The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics spheroidal wave functions in electromagnetic theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations.
Search for library items search for lists search for contacts search for a library. This expansion formula being of very general nature can be transformed to provide many new results involving various commonly used special functions occuring in applied mathematics, mathematics physics and mchanics. The basis for this monograph was work done at stanford research institute for the united states air force cambridge research center under contract af 19 6041296. Spheroidal wave functions download spheroidal wave functions ebook pdf or read online books in pdf, epub, and mobi format. A computational method to calculate the exact solution for. Spheroidal wave functions, integral equation, green function 1. The magic of the prolate spheroidal functions in various setups f. The applicability ranges of the relations obtained are discussed. Flammer spheroidal wave functions stanford university press, stanford. Prolate spheroidal wave functions, fourier analysis and uncertainty iii. Including tables of separation constants and coefficients the mit press stratton, julius a.
A wavelet in the form of the first odd prolate spheroidal wave function is proposed for the wavelet transform of a nonuniform 2d image and the formation of clusters of wavelet coefficients in it. On the evaluation of prolate spheroidal wave functions and. Computational geometric and boundary value properties of oblate spheroidal quaternionic wave functions article in wave motion 57 april 2015 with 36 reads how we measure reads. The dimension of the space of essentially time and bandlimited signals. Stay on top of important topics and build connections by joining wolfram community groups relevant to. They also find considerable application in other areas such as signal processing and. In the next few sections we follow the notation of flammer 3 and slepian 18,19. Stratton 1935, chu and stratton 1941, and rhodes 1970 define the spheroidal functions as those solutions of the differential equation. On the asymptotic expansion of the spheroidal wave function and.
Spheroidal wave functions become elementary if gammanpi2. Download pdf spheroidal wave functions free online new. An introduction discusses the mathematical properties of the functions and describes some of their applications. During the course of finding, we establish several particular cases. While historically the numerical evaluation of pswfs presented serious. Prolate spheroidal wave functions and applications. Spheroidal wave functions in electromagnetic theory nasaads. Intended to facilitate the use and calculation of spheroidal wave functions, this applicationsoriented text features a detailed and unified account of the properties of these functions. Some relations between the spheroidal and spherical wave.
This paper investigates the extent to which a time series can be concentrated on a finite index set and also have its spectrum. Miranian department of mathematics, university of california, berkeley ca, 94720 abstract the singular functions for the problem of recovering a time limited function from its fourier transform in a certain. It can be used in various applications where spheroidal structures are involved and full wave solutions are expected. Asymptotic expansions of angular prolate spheroidal wave functions for large values of. Read generalized prolate spheroidal wave functions for offset linear canonical transform in clifford analysis, mathematical methods in the applied sciences on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
Fourier expansion of generalized prolate spheroidal wave. The prolate spheroidal wave functions are likely to be a better tool for the design of spectral and pseudospectral techniques than the orthogonal polynomials and. Calculation of spheroidal wave functions sciencedirect. Spheroidal wave functions flammer pdf spheroidal wave functions of flammer c. This paper discusses the calculation of spheroidal wave functions by direct numerical methods. Speroidal wave functions occur in many scientific and engineering contexts, from atomic nuclei to the cosmos scattering by nonspherical nuclei, wave functions of diatomic molecules, analysis of bandlimited random noise, orthogonal frequency division multiplexing, and anisotropy of the cosmic microwave background radiation.
Waveletodd prolate spheroidal wave functions in the. There are many fields where spheroidal functions play important roles just as the spherical functions do. Zhang prolate spheroidal wave functions pswfs possess many remarkable properties. Recently, pswfs have been becoming increasingly popular in various areas in which such functions occur this includes physics e. Solutions to this equation constitute an essential element in the numerical calculation of the diffraction, radiation, and scattering of acoustic and electromagnetic waves by spheroids.
What is a prolate spheroid wave function and how does it apply to eegs and brain mapping. Therefore, visualizing these functions and computing them reliably. Wave functions waveguides and cavities scattering separation of variables the special functions vector potentials the spherical bessel equation each function has the same properties as the corresponding cylindrical function. Theory and computation of the spheroidal wave functions arxiv. Flammer, spheroidal wave functions, 1957 are included as a special case of meixners more general functions. Three classic works on spheroidal wave functions are those by stratton 17, meixner 18, and flammer 19, with tables of function values. Aline bonamiaand abderrazek karouib1 a f ed eration denispoisson, mapmoumr 6628, department of mathematics, university of orl eans, 45067 orl eans cedex 2, france. Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and bandlimit. Spheroidal wave functions in electromagnetic theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations. This fact may allow the extension of the current one dimensional model to three dimensions and increase the understanding of analytical features of quantum systems. The functions come from the separation of the helmholtz equation in spheroidal coordinates.
Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a convenient means for handling wave problems in spheroidal coordinates. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a. Prolate spheroidal wave functions, an introduction to the slepian series and its properties. A discrete time series has associated with it an amplitude spectrum which is a periodic function of frequency. Spheroidal wave functions are solutions of the helmholtz equation that are found by writing the equation in spheroidal coordinates and applying the technique of separation of variables, just like the use of spherical coordinates lead to spherical harmonics. Perhaps the most complete description of the spheroidal wave functions is given by flammer 4. Spheroidal wave functions by carson flammer is available.
Prolate spheroidal wave functions, fourier analysis, and uncertainty v. Spheroidal wave functions from wolfram library archive. Addressed to applied mathematicians, mathematical physicists. A complete set of bandlimited functions is described which possesses the curious property of being orthogonal over a given finite interval as well as over. Generalized prolate spheroidal wave functions for offset.
Click download or read online button to spheroidal wave functions book pdf for free now. Carson flammer intended to facilitate the use and calculation of spheroidal wave functions, this applicationsoriented text features a detailed and unified account of the properties of these functions. Acoustic wave propagation features in the spherical coordinate system as a particular case of the prolate spheroidal coordinate system are presented. Prolate spheroidal wave functions whose domain is a portion of the surface of the unit sphere are more generally called slepian functions see also spectral concentration problem. They are called oblate spheroidal wave functions if oblate spheroidal coordinates are used and prolate spheroidal wave functions if prolate. Spheroidal coordinates and wave functions spheroidal. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it discusses separation of the scalar wave equation in spheroidal coordinates, angle and radial functions, integral representations and relationism, and expansions in spherical. Selecting this option will search all publications across the scitation platform selecting this option will search all publications for the publishersociety in context. Prolate spheroidal wave functions, an introduction to the. Additional subjects include recurrence relations of whittaker type, asymptotic expansions for large values of c, and vector wave functions. Prolate spheroidal wave functions, fourier analysis, and. As such, they play an important role in signal processing, fourier analysis, and approximation theory.
The tables were computed to fiveplace accuracy on the whirlwind digital computer, and automatically tabulated. Generalized prolate spheroidal wave functions for offset linear canonical transform in clifford analysis k. Introduction the spheroidal wave equations are extension of the ordinary spherical equations. Spectral decay of the sinc kernel operator and approximations by prolate spheroidal wave functions. There are two kinds of eigenvalues in the differential and corresponding integral equations, and the relation between them is given explicitly. Prolate spheroidal wave function as exact solution of the. Flammer, tables of spheroidal wave functions vychisl.
Intended to facilitate the use and calculation of spheroidal wave functions, this applicationsoriented text features a. Wang, 2017 and they are considered as a particular type of the spheroidal wave functions flammer, 2014. These are of great utility in disciplines such as geodesy or cosmology. They are of interest because spheroids give tractable models for various boundaryvalue problems in electromagnetism and acoustics. This applicationsoriented text features a detailed and unified account of the use and calculation of spheroidal wave functions. The systems must have a common origin of coordinates and a common symmetry axis of coordinate surfaces. Prolate spheroidal wave functions and their properties computation of the pswfs by flammer s method uniform estimates of the pswfs and their derivatives applications of the pswfs wkb method for the pswfs uniform bounds of the pswfs and their derivatives exponential decay of the eigenvalues associated with the pswfs. These are of great utility in disciplines such as geodesy 28 or cosmology. The spheroidal wavefunctions of flammer 1957 spheroidal wave functions are included as a special case of meixners more general functions. Spheroidf is a mathematica package used to compute the eigenvalues of the spheroidal wave equations and angular and radial spheroidal wave functions. Software for computing the spheroidal wave functions. Prolate spheroidal wave functions, fourier analysis and. Rotating sound sources cause the frequency veering phenomenon and change the patterns of psd.
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