메뉴 건너뛰기




Volumn 17, Issue 4, 2001, Pages 633-657

Intertwining relations between the Fourier transform and discrete Fourier transform, the related functional identities and beyond

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035420302     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/17/4/305     Document Type: Article
Times cited : (36)

References (43)
  • 1
    • 0000523068 scopus 로고
    • An algorithm for the machine computation of the complex Fourier series
    • Cooley and Tukey 1965 An algorithm for the machine computation of the complex Fourier series Math. Comput. 19 297-301
    • (1965) Math. Comput. , vol.19 , pp. 297-301
    • Cooley1    Tukey2
  • 3
    • 0003542838 scopus 로고    scopus 로고
    • Quantum computers: Hopes and reality
    • (Moscow: Ijevsk) in Russian
    • Valiev K A and Kokin A A 2001 Quantum computers: hopes and reality Regular and Chaotic Dynamics (Moscow: Ijevsk) (in Russian)
    • (2001) Regular and Chaotic Dynamics
    • Valiev, K.A.1    Kokin, A.A.2
  • 5
    • 0342836170 scopus 로고    scopus 로고
    • Classical computation, quantum computation and Shor's factorisation algorithm
    • Manin Yu 1999 Classical computation, quantum computation and Shor's factorisation algorithm Seminar Bourbaki
    • (1999) Seminar Bourbaki
    • Manin, Yu.1
  • 6
    • 51249180339 scopus 로고
    • Stimulating physics with computers
    • Feynman R 1982 Stimulating physics with computers Int. J. Theor. Phys. 21 467-88
    • (1982) Int. J. Theor. Phys. , vol.21 , pp. 467-488
    • Feynman, R.1
  • 7
    • 5344230456 scopus 로고
    • Quantum mechanical computers
    • Feynman R 1986 Quantum mechanical computers Found. Phys. 16 507-31
    • (1986) Found. Phys. , vol.16 , pp. 507-531
    • Feynman, R.1
  • 8
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorisation and discrete logarithms on a quantum computer
    • Shor P W 1997 Polynomial-time algorithms for prime factorisation and discrete logarithms on a quantum computer SIAM J. Comput. 26 1484-509
    • (1997) SIAM J. Comput. , vol.26 , pp. 1484-1509
    • Shor, P.W.1
  • 12
    • 84966256901 scopus 로고
    • The determination of the Gauss sums
    • Berndt B C and Evans R D 1981 The determination of the Gauss sums J. Am. Math. Soc. 5 107-29
    • (1981) J. Am. Math. Soc. , vol.5 , pp. 107-129
    • Berndt, B.C.1    Evans, R.D.2
  • 13
    • 0342401453 scopus 로고
    • Intorno ad un teorema di Abel
    • Cremona L 1856 Intorno ad un teorema di Abel. Ann. Sci. Mat. Fis. 7 99-105
    • (1856) Ann. Sci. Mat. Fis. , vol.7 , pp. 99-105
    • Cremona, L.1
  • 14
    • 0342836168 scopus 로고    scopus 로고
    • The origin of representation theory
    • Conrad K 1998 The origin of representation theory L'Enseignement Math. 44 361-92
    • (1998) L'Enseignement Math. , vol.44 , pp. 361-392
    • Conrad, K.1
  • 16
    • 0007321815 scopus 로고
    • Some cyclotomic matrices
    • Carlitz L 1959 Some cyclotomic matrices Acta Arithmetica 5 293-308
    • (1959) Acta Arithmetica , vol.5 , pp. 293-308
    • Carlitz, L.1
  • 17
    • 0342836169 scopus 로고
    • Analogues of Poisson summation formula
    • Good I J 1962 Analogues of Poisson summation formula Am. Math. Monthly 69 259-66
    • (1962) Am. Math. Monthly , vol.69 , pp. 259-266
    • Good, I.J.1
  • 18
    • 0015315990 scopus 로고
    • Eigenvalue and eigenvector decomposition of the discrete Fourier transform
    • McClennan J H and Parks T W 1972 Eigenvalue and eigenvector decomposition of the discrete Fourier transform IEEE Trans Audio Electroacoust. 20 66-74
    • (1972) IEEE Trans Audio Electroacoust , vol.20 , pp. 66-74
    • McClennan, J.H.1    Parks, T.W.2
  • 20
    • 0001259168 scopus 로고
    • The eigenvectors of the discrete Fourier transform: A version of the Hermite functions
    • Grunbaum F A 1982 The eigenvectors of the discrete Fourier transform: a version of the Hermite functions J. Math. Anal. Appl. 88 355-63
    • (1982) J. Math. Anal. Appl. , vol.88 , pp. 355-363
    • Grunbaum, F.A.1
  • 21
    • 0004175163 scopus 로고
    • New York: Wiley-Interscience
    • Davis P D 1979 Circulant Matrices (New York: Wiley-Interscience) pp 1-300
    • (1979) Circulant Matrices , pp. 1-300
    • Davis, P.D.1
  • 22
    • 0342401452 scopus 로고
    • Moore-Penrose inverses of block k-circulant matrices
    • Smith R L 1977 Moore-Penrose inverses of block k-circulant matrices J. Linear Alg. Appl. 16 237-45
    • (1977) J. Linear Alg. Appl. , vol.16 , pp. 237-245
    • Smith, R.L.1
  • 23
    • 84966201232 scopus 로고
    • Is computing with the finite Fourier transform pure or applied mathematics?
    • Auslander L and Tolimieri R 1979 Is computing with the finite Fourier transform pure or applied mathematics? Bull. Am. Math. Soc. 1 847-97
    • (1979) Bull. Am. Math. Soc. , vol.1 , pp. 847-897
    • Auslander, L.1    Tolimieri, R.2
  • 24
    • 33645089470 scopus 로고
    • Abelian harmonic analysis, theta functions and function algebras on nilmanifolds
    • Berlin: Springer
    • Auslander L and Tolimieri R 1975 Abelian harmonic analysis, theta functions and function algebras on nilmanifolds Lecture Notes in Math. vol 436 (Berlin: Springer)
    • (1975) Lecture Notes in Math. , vol.436
    • Auslander, L.1    Tolimieri, R.2
  • 25
    • 0041177145 scopus 로고
    • On the eigenvectors of Schur's matrix
    • Morton P 1980 On the eigenvectors of Schur's matrix J. Number Theory 12 122-7
    • (1980) J. Number Theory , vol.12 , pp. 122-127
    • Morton, P.1
  • 27
    • 0001804165 scopus 로고
    • Abelian semi-simple algebras and algorithms for the DFT
    • Auslander L, Feig E and Winograd S 1984 Abelian semi-simple algebras and algorithms for the DFT Adv. Appl. Math. 531-55
    • (1984) Adv. Appl. Math. , vol.5 , pp. 31-55
    • Auslander, L.1    Feig, E.2    Winograd, S.3
  • 28
    • 0039978952 scopus 로고
    • The construction of orthonormal bases diagonalising the DFT
    • Tolimieri R 1984 The construction of orthonormal bases diagonalising the DFT Adv. Appl. Math. 5 56-86
    • (1984) Adv. Appl. Math. , vol.5 , pp. 56-86
    • Tolimieri, R.1
  • 29
    • 0000971063 scopus 로고
    • Observations sur la mécanique quantique finie
    • Balian R and Itzykson C 1986 Observations sur la mécanique quantique finie C. R. Acad. Sci., Paris 303 773-8
    • (1986) C. R. Acad. Sci., Paris , vol.303 , pp. 773-778
    • Balian, R.1    Itzykson, C.2
  • 30
    • 36549101887 scopus 로고
    • Eigenvalues and eigenvectors of the finite Fourier transform
    • Mehta M L 1987 Eigenvalues and eigenvectors of the finite Fourier transform J. Math. Phys. 28 781-5
    • (1987) J. Math. Phys. , vol.28 , pp. 781-785
    • Mehta, M.L.1
  • 31
    • 84938170493 scopus 로고
    • Applications of the fast Fourier transform to computation of Fourier integrals, Fourier series and convolution integrals
    • Cooley J, Lewis P and Welch P 1967 Applications of the fast Fourier transform to computation of Fourier integrals, Fourier series and convolution integrals IEEE Trans. Audio Electroacoust. 15 79-84
    • (1967) IEEE Trans. Audio Electroacoust , vol.15 , pp. 79-84
    • Cooley, J.1    Lewis, P.2    Welch, P.3
  • 32
    • 0037628710 scopus 로고
    • The Fourier transform and the discrete Fourier transform
    • Auslander L and Grunbaum F A 1989 The Fourier transform and the discrete Fourier transform Inverse Problems 5 149-64
    • (1989) Inverse Problems , vol.5 , pp. 149-164
    • Auslander, L.1    Grunbaum, F.A.2
  • 36
    • 0003181695 scopus 로고
    • Some comments on the solvable chiral Potts model
    • Matveev V B and Smirnov A O 1990 Some comments on the solvable chiral Potts model Lett. Math. Phys. 19 179-85
    • (1990) Lett. Math. Phys. , vol.19 , pp. 179-185
    • Matveev, V.B.1    Smirnov, A.O.2
  • 37
    • 0038467404 scopus 로고
    • A quantum mechanical analogue for the q-oscillator
    • Floratos E G 1990 A quantum mechanical analogue for the q-oscillator Phys. Lett. B 251 163-6
    • (1990) Phys. Lett. B , vol.251 , pp. 163-166
    • Floratos, E.G.1
  • 39
    • 0031504497 scopus 로고    scopus 로고
    • A solvable Hamiltonian system: Integrability and action angle variables
    • Karimupur V 1997 A solvable Hamiltonian system: Integrability and action angle variables J. Math. Phys. 38 1577-82
    • (1997) J. Math. Phys. , vol.38 , pp. 1577-1582
    • Karimupur, V.1
  • 40
    • 36549101506 scopus 로고
    • Periodic fixed points of Backlund transformations
    • Weiss J 1987 Periodic fixed points of Backlund transformations J. Math. Phys. 28 2025-38
    • (1987) J. Math. Phys. , vol.28 , pp. 2025-2038
    • Weiss, J.1
  • 43
    • 0345531418 scopus 로고
    • Quantum group and magnetic translations. Bethe ansatz for the Azbel-Hofschtadter problem
    • Wiegmann P and Zabrodin A 1994 Quantum group and magnetic translations. Bethe ansatz for the Azbel-Hofschtadter problem Nucl. Phys. B 422 495-514
    • (1994) Nucl. Phys. B , vol.422 , pp. 495-514
    • Wiegmann, P.1    Zabrodin, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.