Institute of Mathematics and Mechanics

Azerbaijan National Academy of Science

01/03/2019

**Basic scientific achievements**

A new method for the approximate solution of linear singular integral equations is constructed and justified.

We introduce the notions of N-integrability for functions and prove that the Cauchy-type integrals of finite complex measures are Cauchy N-integrals of their boundary values.

**The list of publications at the 5 years published**

- R.A.Aliev, Representability of analytic functions in terms of their boundary values, Math. Notes, 73:1 (2003), 8-20.
- R.A.Aliev, A new constructive method for solving singular integral equations, Math. Notes, 79:6 (2006), 749-770.
- R.A.Aliev, Existence of angular boundary values and Cauchy-Green formula, Journal of Mathematical Physics, Analysis, Geometry, 7:1 (2011), 3-18.
- R.A.Aliev, – integrals and boundary values of Cauchy-type integrals of finite measures, Sbornik: Mathematics, 205:7 (2014), 913-935.
- A.D.Gadjiev, R.A.Aliev, Approximation of analytical functions by -positive linear operators in the closed domain, Positivity, 18:3 (2014), 439-447.
- R.A.Aliev, On Taylor coefficients of Cauchy type integrals of finite complex measures, Complex Variables and Elliptic Equations, 60:12 (2015), 1727-1738.
- A.D.Gadjiev, R.A.Aliev, Approximation of analytic functions in annulus by linear operators, Appl. Math. and Comp., 252 (2015), 438-445.
- R.A.Aliev, On properties of Hilbert transform of finite complex measures, Complex Analysis and Operator Theory, 10:1 (2016), 171-185.
- R.A.Aliev, V.E.Ismailov, On a smoothness problem in ridge function representation, Advances in Applied Mathematics, 73 (2016), 154-169.
- R.A.Aliev, Ch.A.Gadjieva, Approximation of Hypersingular Integral Operators With Cauchy Kernel, Numerical Functional Analysis and Optimization, 37:9 (2016), 1055-1065.
- Akif D. Gadjiev, Rashid A. Aliev, Korovkin type theorem for linear -positive operators in a polydisc of analytical functions, Math. Slovaca, 66:5 (2016), 1179-1186.
- Rashid A. Aliev, Representability of Cauchy-type integrals of finite complex measures on the real axis in terms of their boundary values, Complex Variables and Elliptic Equations, 62:4 (2017), 536-553.
- Rashid A. Aliev, Khanim I. Nebiyeva, The A-integral and restricted Ahlfors–Beurling transform, Integral Transforms and Special Functions, 29:10 (2018), 820-830.
- Rashid A. Aliev, Aysel A. Asgarova, Vugar E. Ismailov, A note on continuous sums of ridge functions, Journal of Approximation Theory, 237 (2019), 210–221.