Is computing with the finite Fourier transform pure or applied mathematics?
HTML articles powered by AMS MathViewer
- by L. Auslander and R. Tolimieri PDF
- Bull. Amer. Math. Soc. 1 (1979), 847-897
References
- Louis Auslander, Lecture notes on nil-theta functions, Regional Conference Series in Mathematics, No. 34, American Mathematical Society, Providence, R.I., 1977. MR 0466409, DOI 10.1090/cbms/034
- L. Auslander and J. Brezin, Translation-invariant subspaces in $L^{2}$ of a compact nilmanifold. I, Invent. Math. 20 (1973), 1–14. MR 322100, DOI 10.1007/BF01405260
- Louis Auslander and Richard Tolimieri, Abelian harmonic analysis, theta functions and function algebras on a nilmanifold, Lecture Notes in Mathematics, Vol. 436, Springer-Verlag, Berlin-New York, 1975. MR 0414785, DOI 10.1007/BFb0069850
- L. Auslander and R. Tolimieri, Algebraic structures for $\bigoplus \sum _{n\geq 1}L^{2}(Z/n)$ compatible with the finite Fourier transform, Trans. Amer. Math. Soc. 244 (1978), 263–272. MR 506619, DOI 10.1090/S0002-9947-1978-0506619-4
- Richard Bellman, A brief introduction to theta functions, Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1961. MR 0125252, DOI 10.1017/s0025557200044491
- A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803
- Jonathan Brezin, Harmonic analysis on nilmanifolds, Trans. Amer. Math. Soc. 150 (1970), 611–618. MR 279244, DOI 10.1090/S0002-9947-1970-0279244-3
- Jonathan Brezin, Harmonic analysis on compact solvmanifolds, Lecture Notes in Mathematics, Vol. 602, Springer-Verlag, Berlin-New York, 1977. MR 0447471, DOI 10.1007/BFb0069793 9. J. W. Cooley, P. A. W. Lewis, and P. P. Welch, Historical notes on the fast Fourier transform, Proc. IEEE 55 (1967), 1675-1677.
- James W. Cooley and John W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19 (1965), 297–301. MR 178586, DOI 10.1090/S0025-5718-1965-0178586-1
- I. J. Good, Analogues of Poisson’s summation formula, Amer. Math. Monthly 69 (1962), 259–266. MR 184006, DOI 10.2307/2312938
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
- Kenneth Ireland and Michael I. Rosen, Elements of number theory. Including an introduction to equations over finite fields, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1972. MR 0554185
- Serge Lang, Algebraic number theory, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0282947 15. J. H. McClellan, Comments on "eigenvector and eigenvalue decomposition of the discrete Fourier transform", IEEE Trans. Audio and Electroacoust. (1972), 65.
- James H. McClellan and Thomas W. Parks, Eigenvalue and eigenvector decomposition of the discrete Fourier transform, IEEE Trans. Audio Electroacoust. AU-20 (1972), no. 1, 66–74. MR 0399751, DOI 10.1109/TAU.1972.1162342
- Hans Rademacher, Lectures on elementary number theory, A Blaisdell Book in the Pure and Applied Sciences, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 0170844
- R. Tolimieri, The multiplicity problem for $4$-dimensional solvmanifolds, Bull. Amer. Math. Soc. 83 (1977), no. 3, 365–366. MR 476917, DOI 10.1090/S0002-9904-1977-14269-9
- André Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 165033, DOI 10.1007/BF02391012
- Shmuel Winograd, On computing the discrete Fourier transform, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 4, 1005–1006. MR 415993, DOI 10.1073/pnas.73.4.1005
- Shmuel Winograd, On computing the discrete Fourier transform, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 4, 1005–1006. MR 415993, DOI 10.1073/pnas.73.4.1005
- Shmuel Winograd, On the number of multiplications necessary to compute certain functions, Comm. Pure Appl. Math. 23 (1970), 165–179. MR 260150, DOI 10.1002/cpa.3160230204
- S. Winograd, Some bilinear forms whose multiplicative complexity depends on the field of constants, Math. Systems Theory 10 (1976/77), no. 2, 169–180. MR 468322, DOI 10.1007/BF01683270
- S. Winograd, On the multiplicative complexity of the discrete Fourier transform, Adv. in Math. 32 (1979), no. 2, 83–117. MR 535617, DOI 10.1016/0001-8708(79)90037-9
Additional Information
- Journal: Bull. Amer. Math. Soc. 1 (1979), 847-897
- MSC (1970): Primary 42A68; Secondary 68A20, 68A10, 10G05, 22E25
- DOI: https://doi.org/10.1090/S0273-0979-1979-14686-X
- MathSciNet review: 546312