Is computing with the finite fourier transform pure or applied mathematics?

Bulletin of the American Mathematical Society

Volumn 1, Issue 6, 1979, Pages 847-898

  Auslander, L ^a,b   Tolimieri, R ^a,b  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966201232     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-1979-14686-X     Document Type: Article

References (24)

1. L. Auslander, Lecture notes on nil-theta functions, CBMS Regional Conf. Ser. in Math. no. 34, Amer. Math. Soc., Providence, R. I., 1977.
2. 1 of a compact nilmanifold. I, Invent. Math. 20 (1973), 1-14.
3. L. Auslander and R. Tolimieri (assisted by H. E. Rauch), Abelian harmonic analysis, theta functions and function algebras on a nilmanifold, Lecture Notes in Math., vol. 436, Springer-Verlag, Berlin and New York, 1975.
4. 2(Z/rì) compatible with the finite Fourier transform, Trans. Amer. Math. Soc. 244 (1978), 263-272.
5. R. Bellman, A brief introduction to theta functions, Holt, Rinehart and Winston, New York, 1961.
6. Z. I. Borevich and I. R. Shafarevich, Number theory, Academic Press, New York, 1966.
7. J. Brezin, Harmonic analysis on nilmanifolds, Trans. Amer. Math. Soc. 150 (1970), 611-618.
8. J. Brezin, Harmonic analysis on compact solvmanifolds, Lecture Notes in Math., vol. 602, Springer-Verlag, Berlin and New York, 1977.
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.
10. J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of conplex Fourier series, Math. Comput. 19 (1965), 297-301.
11. 9s summation formula, Amer. Math. Monthly 69 (1962), 259-266.
12. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Clarendon Press, Oxford, 1938.
13. K. Ireland and M. I. Rosen, Elements of number theory, Bogden and Quigley, New York, 1972.
14. S. Lang, Algebraic number theory, Addison-Wesley, Reading, Mass., 1970.
15. J. H. McClellan, Comments on "eigenvector and eigenvalue decomposition of the discrete Fourier transform", IEEE Trans. Audio and Electroacoust. (1972), 65.
16. J. H. McClellan and T. W. Parks, Eigenvalue and eigenvector decomposition of the discrete Fourier transform, IEEE Trans. Audio and Electroacoust. March (1972), 66-74.
17. H. Rademacher, Lectures on elementary number theory, Blaisdell, Boston, Mass., 1964.
18. R. Tolimieri, The multiplicity problem for 4-dimensional solvmanifolds, Bull. Amer. Math. Soc. 83 (1977), 365-366.
19. 9operateurs unit aires, Acta Math. Ill (1964), 143-211.
20. S. Winograd, On computing the discrete Fourier transform, Proc. Nat. Acad. Sci. U. S. A. 73 (1976), 1005-1006.
21. S. Winograd, On computing the discrete Fourier transform, I. B. M. Research Report, 1976.
22. S. Winograd On the number of multiplications necessary to compute certain functions, Comm. Pure Appl. Math. 23 (1970), 165-179.
23. S. Winograd, Some bilinear forms whose multiplicative complexity depends on the field of constants, Math. Systems Theory 10 (1977), 169-180.
24. S. Winograd, On the multiplicative complexity of the discrete Fourier transform, Advances in Math, (to appear).