Combining Riesz bases

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Avdonin, S.A., Moran, W.: Sampling and interpolation of functions with multi-band spectra and controllability problems. Optimal control of partial differential equations (Chemnitz, 1998). Int. Ser. Numer. Math. 133, 43–51 (1999) (Birkhäuser, Basel)

Avdonin, S.A., Bulanova, A., Moran, W.: Construction of sampling and interpolating sequences for multi-band signals. The two-band case. Int. J. Appl Math. Comput. Sci. 17(2), 143–156 (2007)

Bezuglaya, L., Katsnel’son, V.E.: The sampling theorem for functions with limited multi-band spectrum. Z. Anal. Anwend. 12(3), 511–534 (1993)

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Fuglede, B.: Orthogonal exponentials on the ball. Expo. Math. 19(3), 267–272 (2001)

Hru $$\breve{{\rm s}} \breve{{\rm c}}$$ s ˘ c ˘ ev, S.V., Nikol’skii, N.K., Pavlov, B.S.: Unconditional bases of exponentials and of reproducing kernels. Complex analysis and spectral theory (Leningrad, 1979/1980). In: Lecture Notes in Mathematics, vol. 864, pp. 214–335. Springer, Berlin (1981)

Iosevich, A., Katz, N., Tao, T.: The Fuglede spectral conjecture holds for convex planar domains. Math. Res. Lett. 10(5), 559–569 (2003)

Iosevich, A., Kolountzakis, M.N.: Periodicity of the spectrum in dimension one. Anal. PDE 6(4), 819–827 (2013). arXiv:1108.5689

Kadec’, M.I.: The exact value of the Paley–Wiener constant (in Russian). Dokl. Akad. Nauk. SSSR 155, 1253–1254 (1964) (English translation Sov. Math. Dokl. 5(2), 559–561, 1964)

Katsnel’son, V.E.: Exponential bases in $$L^{2}$$ L 2 (in Russian). Funkc. Anal. Prilož. 5(1), 37–47 (1971). (English translation Funct. Anal. Appl. 5(1), 31–38, 1971)

Katsnel’son, V.E.: Sampling and interpolation for functions with multi-band spectrum: the mean-periodic continuation method. In: Wiener-Symposium (Grossbothen, 1994). Synergie Syntropie Nichtlineare Systeme, vol. 4, pp. 91–132. Verlag Wiss. Leipzig, Leipzig (1996)

Kohlenberg, A.: Exact interpolation of band-limited functions. J. Appl. Phys. 24(12), 1432–1436 (1953)

Kolountzakis, M.N., Matolcsi, M.: Tiles with no spectra. Forum Math. 18(3), 519–528 (2006). arXiv:0406127

Kozma, G., Lev, N.: Exponential Riesz bases, discrepancy of irrational rotations and BMO. J. Fourier Anal. Appl. 17(5), 879–898 (2011). arXiv:1009.2188

Landau, H.J.: Necessary density conditions for sampling and interpolation of certain entire functions. Acta Math. 117, 37–52 (1967)

Lev, N.: Riesz bases of exponentials on multiband spectra. Proc. Am. Math. Soc. 140(9), 3127–3132 (2012). arXiv:1101.3894

Levinson, N.: Gap and density theorems. In: American Mathematical Society Colloquium Publications, vol. 26. American Mathematical Society, New York (1940)

Lyubarskii, Y., Spitkovsky, IM.: Sampling and interpolation for a lacunary spectrum. Proc. R. Soc. Edinb. Sect. A 126(1), 77–87 (1996)

Lyubarskii, Y., Seip, K.: Sampling and interpolating sequences for multi-band-limited functions and exponential bases on disconnected sets. J. Fourier Anal. Appl. 3(5), 597–615 (1997)

Matei, B., Meyer, Y.: Simple quasicrystals are sets of stable sampling. Complex Var. Elliptic Equ. 55(8–10), 947–964 (2010)

Nitzan, S., Olevskii, A.: Revisiting Landau’s density theorems for Paley–Wiener spaces. C. R. Acad. Sci. Paris 350(9–10), 509–512 (2012)

Olevskii, A., Ulanovskii, A.: Uniqueness sets for unbounded spectra. C. R. Acad. Sci. Paris 349(11–12), 679–681 (2011)

Paley, R.E.A.C., Wiener, N.: Fourier transforms in the complex domain. American Mathematical Society Colloquium Publications, vol. 19. American Mathematical Society, New York (1934)

Pavlov, B.S.: The basis property of a system of exponentials and the condition of Muckenhoupt (in Russian). Dokl. Akad. Nauk. SSSR 247, 37–40 (English translation Sov. Math. Dokl. 20, 655–659, 1979) (1979)

Seip, K.: A simple construction of exponential bases in $$L^{2}$$ L 2 of the union of several intervals. Proc. Edinb. Math. Soc. 38(1), 171–177 (1995)

Strichartz, R.S.: Mock Fourier series and transforms associated with certain cantor measures. J. Anal. Math. 81, 209–238 (2000)

Tao, T.: Fuglede’s conjecture is false in 5 and higher dimensions. Math. Res. Lett. 11(2), 251–258 (2004)

Young, R.M.: An Introduction to Nonharmonic Fourier Series (revised first edition). Academic Press Inc., San Diego (2001)