Azerbaijan National Academy of Sciences

- specialty code

- specialty name

- topic name

01.01.02

Differential equations

Completeness and basicity of some special systems

- specialty code

- specialty name

- topic name

01.01.02

Differential equations

Basis properties of the exponent systems and thair generalizations

- date

- specialty name

30.06.2014

Mathematical Analysis

14 

Kostyuchenko problem from the spectral theory of differential operators is completely solved;

classical Paley-Wiener and Bari theorems on bases are generalized with respect to the systems of elements  and the systems of subspaces;

basicity criterion (Riesz basicity in the Hilbert case) for trigonometric systems in Lebesgue spaces with some asymptotics is found (with  T.R.Muradov);

the concept of  “b-basis” generated by some bilinear mapping which generalizes Schauder basis is introduced, classical facts about the theory of bases are extended to this case;

major results on basicity for the systems with infinite defect in subspaces of Banach spaces are obtained (with T.B.Gasymov);

some Banach analogues of the Lax-Milgram theorem are proved;

some complex analogues of well-known Stone-Weierstrass theorem  are proved and extended to the case of the space of piecewise continuous functions;

basis properties of linear phase trigonometric systems are studied in generalized Lebesgue spaces  (with T.R.Muradov, Z.Q.Huseynov, N.P.Nasibova );

an abstract analogue of the Riemann problem is considered, Noetherness of this problem is studied and the obtained results are applied to basis-related problems (with S.R.Sadigova);

the basicity of eigenfunctions of some discontinuous differential operator in Lebesgue spaces is studied (with Ch.M. Hashimov);  

Some analogues of the well-known Kadets ¼-theorem with respect to the systems of exponent, cosines, sines  and some abstract analogues are obtained;

abstract analogues of classical systems of power, sines and cosines are introduced,  a relationship between their basis  properties in Banach spaces is found (with S.R.Sadigova);

space of coefficients  generated by non-degenerate systems, transferred to different mathematical structures,  the generalizations of the theory of analytic functions  is given generated by  nilpotent and idempotent operators, the concept of corresponding bases is introduced (with F.A.Guliyeva, S.R.Sadigova);

basis properties   of double systems consisting of generalized Faber polynomials with complex coefficients on Carleson curve is studied in Lebesgue spaces  (with T.I.Najafov, S.R.Sadigova);

Noetherness   perturbation of Hilbert and Banach frames is studied, the concept of t-frame generated by the Hilbert tensor product is introduced, and its   Noetherness   perturbation is studied (with F.A.Guliyeva);

the basiscity  of the classical exponential systems in Morrey type spaces is proved (with A.A.Guliyeva);

the basis properties of  perturbed trigonometric   systems in weighted generalized Lebesgue spaces are studied (with N.P.Nasibova);

the notion of statistical convergence  is transferred  to the   different mathematical structures,  the notion of μ-statistical convergence and μ-statistical  fundamentality  at the  point in a measurable space are introduced and their equivalence is proved (with S.R.Sadigova, T.Y. Nazarova);

the notion of μ-statistical limits, μ-statistical completeness, μ-statistical fundamentality, μ-statistical equivalence of functions, μ-statistical continuity at infinity are introduced and some properties are studied (with S.R.Sadigova);

the basis  properties of trigonometric perturbed systems in  generalized and weighted generalized Lebesgue spaces are studied (with T.R. Muradov);

signals of solar radiation (total, diffuse and reflected) are  processed by wavelet analysis (with Z.C. Zabidov).

1. Билалов Б.Т.,  “Некоторые вопросы аппроксимации”.  «Элм», 2016, 390 с.
2. Bilalov B.T.,   Nazarova T.Y.  On statistical type convergence in uniform spaces.  Bull. Iranian Math. Soc. Vol. 42 (2016), No. 4, pp. 975–986
3. Билалов Б.Т., Касумов Т.Б. О базисах прямого разложения. Доклады Академии Наук, 2016, том 467, № 4, с. 381–384
4. Bilalov B.T.,   Nazarova T.Y.  Statistical convergence of functional sequences.  Rocky Mountain J. Math., Volume 45, Number 5, 2015, pp. 1413-1423
5. Bilalov B.T.,   Guliyeva  F.A.  t -Frames and their Noetherian Perturbation. Complex Anal. Oper. Theory (2015) 9:1609–1631
6. Bilalov B.T.,   Guliyeva  F.A.  On the basicity property system in the Intuitionistic fuzzy metric space.  Azerbaijan Journal of Mathematics, VOL 4, NO 1 (2014): JANUARY,  pp.136-149
7. Bilalov B.T., Guliyeva F.A. A completeness criterion for a double system of powers with degenerate coefficients , Siberian Mathematical Journal, vol.54, No. 3, 2013
8. Bilalov B.T., Najafov T.I. On basicity of systems of generalized Faber polynomials. Jaen J. Approx. Volume 5, Number 1 (2013), pp. 19-34
9. Bilalov B.T., Guliyeva F.A. Noetherian perturbation of frames. Pensee Journal, vol. 75. isssue 12, 2013, pp.425-431
10. Bilalov B.T.,   Sadigova S.R.  On -statistical convergence. Proceedings of the American Mathematical Society. Vol.143, No. 9, September 2015, pp. 3869–3878
11. Bilalov B.T.,   Kasumov T.B. On Kostyuchenko Problem.  Proceedings of the Institute of Mathematics and Mechanics, NationalAcademy of Sciences of Azerbaijan. Volume 40, Special Issue, 2014, pp. 86-107
12. Bilalov B.T., Guliyeva F.A. On The Frame Properties of Degenerate System of Sines, Journal of Function Spaces and Applications, Vol. 2012 (2012), Article ID 184186, 12 pages

- Reviewer of the Science Development Foundation under the President of the Republic of Azerbaijan ;

-  Chief of the Actuarial Society of Azerbaijan;

- Chairman of the Expert Council  on mathematics and mechanics of Higher Attestation Commission under President of Azerbaijan;

- A member of the Board of the Azerbaijan Mathematical Society ;

- A member of the Coordinating Council for Science under the President of the NAS of Azerbaijan;

- Deputy Chairman of the Council on Problems of Mathematics;

- Editor in Chief  of Azerbaijan Journal of Mathematics;

- Editor in Chief  of Caspian Journal of Applied Mathematics, Ecology and Economics;

- Member of the Board of Mathematical Society of Turkic countries (2009-2011);

- Chairman of the seminar at the Doctoral Dissertation Council,  Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan (2009-2011);

- Member of the Doctoral Dissertation Council at the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan.

Member of the editorial board of scientific journals on mathematics:

- Azerbaijan Journal of Mathematics;

- Caspian Journal of Applied Mathematics, Ecology and Economics;

- Transactions  of the Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan;

- Proceedings of the Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan;

- TWMS Journal of Pure and Applied Mathematics;

- Sahand Communications in Mathematical Analysis (SCMA);

- International Journal of Mathematical Analysis;

- Advances in  Analysis;

- The Aligarh Bulletin of mathematics.

Reviewer of the authorative international journals on mathematics:

- American Mathematical Society;

- Applied Mathematics Letters (Elsevier);

- Proceedings of the Estonian Academy of Sciences ;

- Journal of Applied Mathematics and Computing (Springer);

- Zentralblatt MATH;

- British Journal of Mathematics & Computer Science;

- Sahand Communications in Mathematical Analysis (SCMA);

- Wavelet and Linear Algebra;

- Applied Mathematical Sciences;

- International Journal of Mathematical Analysis;

- Asian Journal of Mathematics and Computer Research;

- Advances in  Analysis.