Frame properties of a part of an exponential system with degenerate coefficients in Hardy classes

References

[1] K. I. Babenko, On conjugate functions (in Russian), Doklady Akad. Nauk SSSR (N. S.) 62 (1948), 157–160. Search in Google Scholar

[2] N. Bary, Sur les bases dans l’espace de Hilbert, C. R. Doklady Acad. Sci. URSS (N. S.) 54 (1946), 379–382. Search in Google Scholar

[3] B. T. Bilalov, The basis property of some systems of exponentials of cosines and sines (in Russian), Differ. Uravn. 26 (1990), no. 1, 10–16; translation in Differ. Equ. 26 (1990), no. 1, 8–13. Search in Google Scholar

[4] B. T. Bilalov, Basis properties of some systems of exponentials, cosines, and sines (in Russian), Sibirsk. Mat. Zh. 45 (2004), no. 2, 264–273; translation in Sib. Math. J. 45 (2004), no. 2, 214–221. 10.1023/B:SIMJ.0000021278.64966.d7Search in Google Scholar

[5] B. T. Bilalov and Z. A. Gasimov, On completeness of exponent system with complex coefficients in weight spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 25 (2005), no. 7, 9–14. Search in Google Scholar

[6] B. Bilalov and F. Guliyeva, On the frame properties of degenerate system of sines, J. Funct. Spaces Appl. 2012 (2012), Article ID 184186. 10.1155/2012/184186Search in Google Scholar

[7] B. T. Bilalov and S. G. Veliev, Bases of the eigenfunctions of two discontinuous differential operators (in Russian), Differ. Uravn. 42 (2006), no. 10, 1428–1430; translation in Differ. Equ. 42 (2006), no. 10, 1503–1506. 10.1134/S0012266106100156Search in Google Scholar

[8] O. Christensen, An Introduction to Frames and Riesz Bases, Appl. Numer. Harmon. Anal., Birkhäuser, Boston, 2003. 10.1007/978-0-8176-8224-8Search in Google Scholar

[9] R. Edwards, Fourier Series with a Modern Exposition. Vol. 1 (in Russian), Mir, Moscow, 1985. Search in Google Scholar

[10] R. Edwards, Fourier Series with a Modern Exposition. Vol. 2 (in Russian), Mir, Moscow, 1985. Search in Google Scholar

[11] V. F. Gaposhkin, A generalization of the theorem of M. Riesz on conjugate functions (in Russian), Mat. Sb. (N. S.) 46(88) (1958), 359–372. Search in Google Scholar

[12] G. J. Garnett, Bounded Analytic Functions (in Russian), Mir, Moscow, 1984; translation, Academic Press, New York, 1981. Search in Google Scholar

[13] C. Heil, A Basis Theory Primer. Expanded edition, Appl. Numer. Harmon. Anal., Birkhäuser, New York, 2011. 10.1007/978-0-8176-4687-5Search in Google Scholar

[14] K. S. Kazaryan and P. I. Lizorkin, Multipliers, bases and unconditional bases of the weighted spaces B and SB (in Russian), Tr. Mat. Inst. Steklov. 187 (1989), 98–115; translation in Proc. Steklov Inst. Math. 1990, no. 3, 111–130. Search in Google Scholar

[15] M. G. Krein, Functional Analysis (in Russian), Nauka, Moscow, 1964. Search in Google Scholar

[16] P. Kusis, Introduction to Hp spaces (in Russian), Mir, Moscow, 1984. Search in Google Scholar

[17] Z. V. Mamedova, On approximate properties of systems in Banach spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 30 (2010), no. 1, 133–138. Search in Google Scholar

[18] Z. V. Mamedova, On basis properties of degenerate exponential system, Appl. Math. 3 (2012), no. 12, 1963–1966. 10.4236/am.2012.312269Search in Google Scholar

[19] E. I. Moiseev, On the basis property of sine and cosine systems in a weighted space (in Russian), Differ. Uravn. 34 (1998), no. 1, 40–44, 141; translation in Differ. Equ. 34 (1998), no. 1, 39–43. Search in Google Scholar

[20] E. I. Moiseev, The basis property of a system of eigenfunctions of a differential operator in a weighted space (in Russian), Differ. Uravn. 35 (1999), no. 2, 200–205, 286; translation in Differ. Equ. 35 (1999), no. 2, 199–204. Search in Google Scholar

[21] E. I. Moiseev and N. Abbasi, On the basis property of the eigenfunctions of a generalized gas-dynamic problem of Frankl’ (in Russian), Dokl. Akad. Nauk 436 (2011), no. 4, 439–442; translation in Dokl. Math. 83 (2011), no. 1, 72–75. Search in Google Scholar

[22] E. I. Moiseev and V. E. Ambartsumyan, On the solvability of a nonlocal boundary value problem with opposite fluxes on a part of the boundary and of the adjoint problem (in Russian), Differ. Uravn. 46 (2010), no. 6, 883–886; translation in Differ. Equ. 46 (2010), no. 6, 892–895. 10.1134/S0012266110060121Search in Google Scholar

[23] S. S. Pukhov and A. M. Sedletskiĭ, Bases of exponentials, sines, and cosines in weighted spaces on a finite interval (in Russian), Dokl. Akad. Nauk 425 (2009), no. 4, 452–455; translation in Dokl. Math. 79 (2009), no. 2, 236–239. Search in Google Scholar

[24] A. Rahimi, Frames and Their Generalizations in Hilbert and Banach Spaces, Lambert Academic Publishing, Saarbrücken, 2011. Search in Google Scholar

[25] W. Rudin, Functional Analysis (in Russian), Mir, Moscow, 1975. Search in Google Scholar

[26] I. Singer, Bases in Banach Spaces. I, Grundlehren Math. Wiss. 154, Springer, New York, 1970. 10.1007/978-3-642-51633-7Search in Google Scholar

[27] A. Zygmund, Trigonometric Series. Vol. I (in Russian), Mir, Moscow, 1965. Search in Google Scholar

[28] A. Zygmund, Trigonometric Series. Vol. II (in Russian), Mir, Moscow, 1965. Search in Google Scholar