About the Project

harmonic analysis


(0.001 seconds)

1—10 of 16 matching pages

1: Donald St. P. Richards
Richards has published numerous papers on special functions of matrix argument, harmonic analysis, multivariate statistical analysis, probability inequalities, and applied probability. He is editor of the book Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, published by the American Mathematical Society in 1992, and coeditor of Representation Theory and Harmonic Analysis: A Conference in Honor of R. A. Kunze (with T. …
2: 15.17 Mathematical Applications
§15.17(iii) Group Representations
For harmonic analysis it is more natural to represent hypergeometric functions as a Jacobi function (§15.9(ii)). …Harmonic analysis can be developed for the Jacobi transform either as a generalization of the Fourier-cosine transform (§1.14(ii)) or as a specialization of a group Fourier transform. …
3: Tom H. Koornwinder
Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. …
4: Bibliography T
  • A. Terras (1988) Harmonic Analysis on Symmetric Spaces and Applications. II. Springer-Verlag, Berlin.
  • T. Ton-That, K. I. Gross, D. St. P. Richards, and P. J. Sally (Eds.) (1995) Representation Theory and Harmonic Analysis. Contemporary Mathematics, Vol. 191, American Mathematical Society, Providence, RI.
  • 5: Bibliography W
  • G. Weiss (1965) Harmonic Analysis. In Studies in Real and Complex Analysis, I. I. Hirschman (Ed.), Studies in Mathematics, Vol. 3, pp. 124–178.
  • E. T. Whittaker (1902) On the functions associated with the parabolic cylinder in harmonic analysis. Proc. London Math. Soc. 35, pp. 417–427.
  • 6: Bibliography H
  • L. K. Hua (1963) Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains. Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI.
  • 7: Bibliography M
  • T. M. MacRobert (1967) Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications. 3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.
  • I. Marquette and C. Quesne (2013) New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. J. Math. Phys. 54 (10), pp. Paper 102102, 12 pp..
  • I. Marquette and C. Quesne (2016) Connection between quantum systems involving the fourth Painlevé transcendent and k -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial. J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
  • G. Matviyenko (1993) On the evaluation of Bessel functions. Appl. Comput. Harmon. Anal. 1 (1), pp. 116–135.
  • J. N. McDonald and N. A. Weiss (1999) A Course in Real Analysis. Academic Press Inc., San Diego, CA.
  • 8: Bibliography L
  • H. A. Lauwerier (1974) Asymptotic Analysis. Mathematical Centre Tracts, Mathematisch Centrum, Amsterdam.
  • L.-W. Li, M. Leong, T.-S. Yeo, P.-S. Kooi, and K.-Y. Tan (1998a) Computations of spheroidal harmonics with complex arguments: A review with an algorithm. Phys. Rev. E 58 (5), pp. 6792–6806.
  • L.-W. Li, T. S. Yeo, P. S. Kooi, and M. S. Leong (1998b) Microwave specific attenuation by oblate spheroidal raindrops: An exact analysis of TCS’s in terms of spheroidal wave functions. J. Electromagn. Waves Appl. 12 (6), pp. 709–711.
  • C. Liaw, L. L. Littlejohn, R. Milson, and J. Stewart (2016) The spectral analysis of three families of exceptional Laguerre polynomials. J. Approx. Theory 202, pp. 5–41.
  • M. J. Lighthill (1958) An Introduction to Fourier Analysis and Generalised Functions. Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York.
  • 9: Bibliography F
  • P. Falloon (2001) Theory and Computation of Spheroidal Harmonics with General Arguments. Master’s Thesis, The University of Western Australia, Department of Physics.
  • J. Faraut and A. Korányi (1994) Analysis on Symmetric Cones. Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford-New York.
  • P. Flajolet and A. Odlyzko (1990) Singularity analysis of generating functions. SIAM J. Discrete Math. 3 (2), pp. 216–240.
  • K. W. Ford and J. A. Wheeler (1959b) Application of semiclassical scattering analysis. Ann. Physics 7 (3), pp. 287–322.
  • L. Fox and I. B. Parker (1968) Chebyshev Polynomials in Numerical Analysis. Oxford University Press, London.
  • 10: 10.73 Physical Applications
    Bessel functions first appear in the investigation of a physical problem in Daniel Bernoulli’s analysis of the small oscillations of a uniform heavy flexible chain. … Consequently, Bessel functions J n ( x ) , and modified Bessel functions I n ( x ) , are central to the analysis of microwave and optical transmission in waveguides, including coaxial and fiber. … Bessel functions enter in the study of the scattering of light and other electromagnetic radiation, not only from cylindrical surfaces but also in the statistical analysis involved in scattering from rough surfaces. … With the spherical harmonic Y , m ( θ , ϕ ) defined as in §14.30(i), the solutions are of the form f = g ( k ρ ) Y , m ( θ , ϕ ) with g = 𝗃 , 𝗒 , 𝗁 ( 1 ) , or 𝗁 ( 2 ) , depending on the boundary conditions. … The analysis of the current distribution in circular conductors leads to the Kelvin functions ber x , bei x , ker x , and kei x . …