Geodesic
The discrete Fourier transform and cyclic convolution on integral lattices
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 443-460 Cet article a éte moissonné depuis la source Math-Net.Ru

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A discrete Fourier transform and a cyclic convolution are constructed on an arbitrary integral lattice. The construction includes as a special case the usual discrete Fourier transform and the usual cyclic convolution. Applications to questions of interpolation of functions and digital signal processing are considered. Methods in the spectral theory of automorphic functions are used to investigate questions in approximation of arbitrary lattices by integral lattices. Bibliography: 14 titles. 
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     author = {V. A. Bykovskii},
     title = {The discrete {Fourier} transform and cyclic convolution on integral lattices},
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V. A. Bykovskii. The discrete Fourier transform and cyclic convolution on integral lattices. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 443-460. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a10/

[1] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii I, Nauka, M., 1973

[2] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1985 | MR | Zbl

[3] Dobrovolskii N. P., Otsenki otklonenii obobschennykh parallelepipedalnykh setok, Dep. No 6089-84, VINITI, M., 1984

[4] Kassels D., Ratsionalnye kvadratichnye formy, Mir, M., 1982 | MR

[5] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize., Fizmatgiz, M., 1963 | MR

[6] Kuznetsov N. V., “Gipoteza Peterssona dlya parabolicheskikh form vesa nul i gipoteza Linnika. I. Summa summ Klostermana”, Matem. sb., 111(153) (1980), 334–383 | MR | Zbl

[7] Makklellan Dzh. X., Reider Ch. M., Primenenie teorii chisel v tsifrovoi obrabotke signalov, Radio i svyaz, M., 1983

[8] Nussbaumer G., Bystroe preobrazovanie Fure i algoritmy vychisleniya svertok, Radio i svyaz, M., 1985 | MR | Zbl

[9] Podsypanin E. V., “Raspredelenie tselykh tochek na determinantnoi poverkhnosti”, Issledovaniya po teorii chisel. 6, Zap. nauch. seminarov LOMI, 93, 1980, 30–40 | MR | Zbl

[10] Skubenko F. B., “K raspredeleniyu tselochislennykh matrits i vychisleniyu ob'ema fundamentalnoi oblasti unimodulyarnoi gruppy matrits”, Tr. MIAN, 80, 1965, 129–144 | MR | Zbl

[11] Sobolev S. L., Vvedenie v teoriyu kubaturnykh formul, Nauka, M., 1974 | MR

[12] Hlawka E., “Zur angenäherten Berechnung mehrfacher Integrale”, Monatsh. Math., 66:6 (1962), 140–151 | DOI | MR | Zbl

[13] Selberg A., “Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series”, J. Indian Math. Soc., 20 (1956), 47–87 | MR | Zbl

[14] Moreno C. J., Shahidi F., “The $L$-functions $L\bigl(s,Sym^m(r),\pi\bigr)$”, Can. Math. Bull., 28:4 (1985.), 405–410 | MR | Zbl