Journal Papers

* An elementary proof of the polynomial matrix spectral factorization theorem, to be published in Proc. Roy. Soc. Edinburgh, Sect. A.

* On compact wavelet matrices of rank m and of order and degree N, (with E. Lagvilava) to be published in J. Fourier Anal. Appl.

* Matrix spectral factorization and wavelets, (with G. Janashia and E. Lagvilava) J. of Math. Sci. (N.Y.) . 195 (2013), no. 4, 445-453, DOI: 10.1007/s10958-013-1589-x

* An approximation of Daubechies wavelet matrices by perfect reconstruction filter banks with rational coefficients, (with A. Gamkrelidze, and E. Lagvilava) Adv. Comput. Math.  38 (2013), no.1, 147-158,   DOI: 10.1007/s10444-011-9232-1

* A remark on a polynomial matrix factorization theorem, (with I. M. Spitkovsky) Georgian Math. J. 19 (2012), 489-495.

* On approximate spectral factorization of matrix-functions, (with G. Janashia and E. Lagvilava) J. Fourier Anal. Appl. 17 (2011), no. 5, 976-990, DOI: 10.1007/s00041-010-9167-9

* A new method of matrix spectral factorization, (with G. Janashia and E. Lagvilava) IEEE Trans. Inform. Theory  57 (2011), no. 4, 2318-2326,  DOI: 10.1109/TIT.2011.2112233

*  On the Uniqueness Property of Various Maximal Operators, Res. Inst. Math. Sci. (RIMS), Kyoto, B22 (2010), 137-144.

* Remark on outer analytic matrix-functions, (with E. Lag­vi­la­va) Proc. A. Razmadze Math. Inst. 152 (2010), 29-32.

* A simple proof of matrix-valued Fejer-Riesz theorem, (with G. Janashia and E. Lag­vi­la­va)  J. Fourier Anal. Appl. 14 (2009), 124-127 (DOI: 10.1007/s00041-008-9051-z).

* The John-Nirenberg inequality for ergodic systems, (with N. Fujii) Far East J. Dyn. Syst. 11 (2009), 49-56.

* On parametrization of compact wavelet matrices, (with E. Lagvilava) Bull. Georgian Acad. Sci. 2(4) (2009), 23-28.

* Fractional, maximal and singular operators in variable exponent Lorentz spaces, (with V. Kokilashvili and S.G. Samko) Fract. Calc. Appl. Anal. 11 (2008), 407-420.

* On the uniqueness of the one-sided maximal functions of Borel measures, (with N. Fujii) J. Math. Soc. Japan, 60 (2008), 695-717.

* An analytic proof of the matrix spectral factorization theorem, (with G. Janashia and E. Lag­vi­la­va)  Georgian Math. J. 15 (2008), 241-249.

* The Riesz “rising sun” lemma for arbitrary Borel measures with some applications, (with N. Fujii and Y. Terasawa)  J. Funct. Spaces Appl. 5 (2007), 319-331.

* On the generalization of the Riesz-Zygmund theorem for the ergodic Hilbert transform, (with R. Sato) Ergodic Theory Dynam. Systems, 27 (2007), 113-122. 

* A weighted ergodic maximal equality for nonsingular semiflows, (with R.Sato)  Colloq. Math. 103 (2005), 207-213.  

* On the uniqueness of the two-sided ergodic maximal function, Georgian Math. J. 12 (2005), 45-52.

* A new computational algorithm of spectral factorization for polynomial matrix functions, (with G. Janashia and E. Lagvilava) Proc. A. Razmadze Math. Inst. 136 (2004), 41-46.

* The Stein-Weiss theorem for the ergodic Hilbert transform, Studia Math. 165, (2004), 61-71.

* A new proof of the Ergodic Maximal Equality, Real Anal. Exchange, 29 (2003/04), 409-411.

* The generalization of Stein-Weiss Theorem for the ergodic Hilbert transform, Studia Math. 155 (2003), 67-75.

* On the Ergodic Maximal Equality, Proc. A. Razmadze Math. Inst. 132 (2003), 89-92.

* On the uniqueness of the ergodic maximal function, Fund. Math. 174 (2002), 217- 228.

* On the uniqueness of maximal operators for ergodic flows, Rev. Mat. Complut. 15 (2002), 75-84.

* The rearrangement inequality for the ergodic maximal function, Georgian Math. J. 8 (2001), 727-732.

* On approximate factorization of positive definite matrix functions, (with G. Janashia and E. Lagvilava) Uspekhi Mat. Nauk, 54 (1999), 161-162 (in Russian). Translated as Russian Math. Surveys, 54 (1999), 1246-1247. 

* On approximate factorization of positive definite matrix functions of second order, Proc. A. Razmadze Math. Inst. 120 (1999), 49-56.

* On reverse weak (1,1) type inequalities for the maximal operators with respect to ar­bi­t­ra­ry measures, Real Anal. Exchange, 24 (1998/9), No. 2, 761-764.

* On the factorization of unitary matrix-functions, (with G. Janashia and E. Lagvilava)  Proc. A. Razmadze Math. Inst. 116 (1998), 101-106.

* On the integrability of the ergodic Hilbert transform for a class of functions with equal a­bsolute values, Georgian Math. J. 5 (1998), 101-106.

* On approximate factorization of the spectral measures of stationary processes, Proc A. Raz­madze Math. Inst. Georgian Acad. Sci. 114 (1997), 35-38.

* Uniqueness theorem for maximal functions, Georgian Math. J. 3 (1996), 49-52.

* On a relationship between the integrabilities of various maximal functions, Georgian Math. J. 2 (1995), 9-20.

* On the integrability of the ergodic maximal function, Proc. A. Razmadze Math. Inst. Georgian Acad. Sci. 102 (1993), 29-40.

* A remark on a theorem of Atkinson, Proc. A. Razmadze Math. Inst. Georgian Acad. Sci. 101 (1992), 39-45.

* On the distribution function of the majorant of ergodic means, Studia Math. 103 (1992), 1-15.

* On the majorant of ergodic means (continuous case),  Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruz. SSR  98 (1990), 112-124 (in Russian). 

* On the majorant of ergodic means, Uspekhi Mat. Nauk, 45 (1990), No. 2 (272), 223-224 (in Russian). Translated as Russian Math. Surveys, 45, (1990), 209-211. 

* On the convergence of Fourier-Walsh series in the space L, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruz. SSR, 95 (1989), 71-80 (in Russian).  

* On the convergence of Fourier series in L, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruz. SSR, 89 (1988), 83-94 (in Russian).

Conference Papers

* On the uniqueness property of various maximal operators, to appear in Proceedings of Symposiums of Research Institute of Mathematical Sciences, Kyoto, Japan.

*  On the estimation of the convergence rate in the Janashia-Lagvilava spectral factorization algorithm, (with N. Fujii) to appear in Proceedings of the Harmonic Analysis and its Applications at Sapporo 2007, Sept. 2-4, Hokkaido University, pp. 24-32.  http://arxiv.org/abs/0711.2554.

* A new efficient matrix spectral factorization algorithm, (with G. Janashia and E. Lag­vi­la­va) SICE Annual Conference 2007, Sept. 17-20, Kagawa University, Japan, pp. 20-24 (CD-ROM). 

Abstracts and Short Communications

* On spectral factorization of matrix functions, (with G. Janashia and E. Lag­vi­la­va) Rep. Sem. Appl. Math. Inst. 25 (2011), 34-38.

* On parametrization of compact wavelet matrices, (with E. Lagvilava) Bull. Georgian Acad. Sci. 2(4) (2008), 23-28.

* The John-Nirenberg inequality for ergodic systems, (with N. Fujii) Annual Meeting of Mathematical Society of Japan, Sendai, September, 2007, Session of real analysis, Abstracts of talks, 7-8.

* On the generalizations of the Riesz “rising sun” lemma, Real Analysis Symposium, October 27-29, 2006, Hirosaki University Press, 65-68.

* On the uniqueness of maximal functions of Borel measures, (with N. Fujii)  Annual Meeting of Mathematical Society of Japan, Osaka, Sept. 2006, Session of real analysis, Abstracts of talks, 11-12.?

* On the boundedness of the ergodic Hilbert transform in Lorentz spaces, (with T. Sobukawa) Proc. A. Razmadze Math. Inst. 140 (2006), 160-161.?

* On the generalization of the Riesz-Zygmund theorem for the ergodic Hilbert transform, (with R. Sato)  Annual Meeting of Mathematical Society of Japan, Tokyo, March 2005, Session of real analysis, Abstracts of talks, 23-24.

* On a relationship between the integrabilities of various ergodic maximal functions, Proc. A. Razmadze Math. Inst. 132 (2003), 141-142.

* A new multivariate spectral factorization algorithm, (with G. Janashia and E. Lag­vi­la­va) First SIAM-EMS Conference “Applied Mathematics in our Changing World”, Col­lec­tion of Abstracts, Berlin, 2001, p.61.

* On reverse weak (1.1) inequalities for the maximal operators with respect to arbitrary me­asures, Proc. A. Razmadze Math. Inst. 117 (1998), 119-120.

* On a relationship between the integrabilities of various maximal functions, Rep. Sem. Appl. Math. Inst. 9 (1994), No. 1-3, 22-23.

* A new proof of a theorem of Atkinson, Rep. Sem. Appl. Math. Inst. 7 (1992), No. 2, 63-64.

* On the integrability of the ergodic maximal function, Soobshch. Akad. Nauk Gruz. SSR 139 (1990), No. 1, 49-51.

* On the distribution function of the majorant of ergodic means, Seminar Inst. Prikl. Mat. Tbilis. Univ. 3 (1988), No. 2, 89-92 (in Russian).

* On the convergence of Fourier-Walsh series in the space L, Soobshch. Acad. Nauk. Gruz. SSR, 130 (1988), No.2, 249-251 (in Russian). 

* On the convergence of Fourier series in the space L, Soobshch. Acad. Nauk. Gruz. SSR, 126 (1988), No.3, 481-483 (in Russian).