Arkiv för Matematik

  • Ark. Mat.
  • Volume 38, Number 1 (2000), 139-170.

Complete interpolating sequences for Fourier transforms supported by convex symmetric polygons

Yurii I. Lyubarskii and Alexander Rashkovskii

Full-text: Open access

Article information

Source
Ark. Mat., Volume 38, Number 1 (2000), 139-170.

Dates
Received: 8 October 1998
Revised: 29 March 1999
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898671

Digital Object Identifier
doi:10.1007/BF02384495

Mathematical Reviews number (MathSciNet)
MR1749363

Zentralblatt MATH identifier
1038.42011

Rights
2000 © Institut Mittag-Leffler

Citation

Lyubarskii, Yurii I.; Rashkovskii, Alexander. Complete interpolating sequences for Fourier transforms supported by convex symmetric polygons. Ark. Mat. 38 (2000), no. 1, 139--170. doi:10.1007/BF02384495. https://projecteuclid.org/euclid.afm/1485898671


Export citation

References

  • Benedetto, J., Irregular sampling and frames, in Wavelets (Chui, C., ed.), pp. 445–507, Academic Press, Boston, Mass., 1992.
  • Beurling, A., Mittag-Leffler lectures on harmonic analysis, in Collected Works of Arne Beurling, vol 2, pp. 341–365, Birkhäuser, Boston, Mass., 1989.
  • Duffin, R. J. and Shaeffer, A. C., A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341–366.
  • Gruman, L., The regularity of growth of entire functions whose zeros are hyperplanes, Ark. Mat. 10 (1972), 23–31.
  • Gruman, L., Interpolation in spaces of entire functions in CnCanad. Math. Bull. 19 (1976), 109–112.
  • Higgins, J., Five short stories about cardinal series, Bull. Amer. Math. Soc. 12 (1985), 45–89.
  • Khrushchev, S. V., Nikolski, N. K. and Pavlov, B. S., Unconditional bases of exponentials and of reproducing kernels, in Complex Analysis and Spectral Theory (Havin, V. P. and Nikolski, N. K., eds.), Lecture Notes in Math. 864, pp. 214–335, Springer-Verlag, Berlin-Heidelberg, 1981.
  • Landau, H. J. Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967), 37–52.
  • Levin, B. Ya., On bases from exponential functions in L2, Zap. Mekh.-Mat. Fak. i Khar'kov. Mat. Obshch. 27 (1961), 39–48 (Russian).
  • Levin, B. Ya., Lectures on Entire Functions, Amer. Math. Soc., Providence, R. I., 1996.
  • Logvinenko, V. N., Interpolation of entire functions of several variables, Dokl. Akad. Nauk SSSR 234 (1977), 302–304. (Russian). English transl. Soviet Math. Dokl. 18 (1977), 659–661.
  • Logvinenko, V. N. and Sereda, Yu. F., Equivalent norms in spaces of entire functions of exponential type, Teor. Funktsiî Funktsional. Anal. i Prilozhen. 20 (1974), 62–78 (Russian).
  • Lyubarskii, Yu. and Seip, K., Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt (Ap) condition, Rev. Mat. Iberoamericana 3 (1997), 361–376.
  • Minkin, A. M., Reflection of exponents, and unconditional bases of exponentials, Algebra i Analiz 3:5 (1991), 109–134 (Russian). English transl.: St. Petersburg Math. J. 3 (1992), 1043–1068.
  • Nikolski, N. K., Bases of exponentials and values of reproducing kernels, Dokl. Akad. Nauk SSSR 252 (1980), 1316–1320 (Russian). English transl.: Soviet Math. Dokl. 21 (1980), 937–941.
  • Nikolski, N. K., Treatise on the Shift Operator, Springer-Verlag, Berlin-Heidelberg, 1986.
  • Paley, R. E. A. C. and Wiener, N., Fourier Transforms in the Complex Domain, Amer. Math. Soc. Colloq. Publ. 19, Amer. Math. Soc., New York, 1934.
  • Papush, D. E., The growth of entire functions with “plane” zeros, Teor. Funktsiî Funktsional. Anal. i Prilozhen. 48 (1987), 117–125 (Russian).
  • Papush, D. E., An analog of the Lagrange interpolation series for a sequence of points in Cl in Operator Theory, Subharmonic Functions (Marchenko, V. A., ed.), pp. 75–84, Naukova Dumka, Kiev, 1991 (Russian).
  • Papush, D. E., Interpolation with discrete sets in Cl, Teor. Funktsiî Funktsional. Anal. i Prilozhen. 55 (1991), 113–124 (Russian). English transl.: J. Soviet Math. 59 (1992), 666–674.
  • Papush, D. E. and Russakovskii, A. M., Interpolation on plane sets in C2, Ann. Fac. Sci. Toulouse Math. 1 (1992), 337–362.
  • Pavlov, B. S., The basis property of a system of exponentials and the condition of Muckenhoupt, Dokl. Akad. Nauk SSSR 247 (1979), 37–40 (Russian). English transl.: Soviet Math. Dokl. 20 (1979), 655–659.
  • Ronkin, L. I., Elements of the Theory of Analytic Functions of Several Variables, Naukova Dumka, Kiev, 1977 (Russian).
  • Sekerin, A. B., Construction of entire functions with prescribed growth, Sibirsk. Mat. Zh. 27 (1986), 179–192, 225 (Russian). English transl: Siberian Math. J., 27 (1986), 454–456.
  • Sekerin, A. B., On the representation of analytic functions of several varables by exponential series, Izv. Ross. Akad. Nauk Ser. Mat. 56:3 (1992), 538–565 (Russian). English transl.: Russian Acad. Sci. Izv. Math. 40 (1993), 503–527.
  • Wiegerinck, J. J. O. O., Growth properties of Paley-Wiener functions on Cn, Nederl. Akad. Wetensch. Proc. Ser. A 87 (1984), 95–112.