approximation theory, real and complex analysis, functional analysis
Main publications:
V. E. Ismailov, “A three layer neural network can represent any multivariate function”, J. Math. Anal. Appl., 523:1 (2023), Paper No. 127096
V. E. Ismailov, Ridge functions and applications in neural networks, Mathematical Surveys and Monographs, 263, American Mathematical Society, Providence, 2021 , 186 pp. https://bookstore.ams.org/surv-263
R. A. Aliev, V. E. Ismailov, “A representation problem for smooth sums of ridge functions”, J. Approx. Theory, 257 (2020), 105448, 13 pp.
A. Kh. Asgarova, V. E. Ismailov, “On the representation by sums of algebras of continuous functions”, C. R. Math. Acad. Sci. Paris, 355:9 (2017), 949–955
A. Kh. Asgarova, V. E. Ismailov, “Diliberto-Straus algorithm for the uniform approximation by a sum of two algebras.”, Proc. Indian Acad. Sci. Math. Sci., 127:2 (2017), 361–374
V. E. Ismailov, “Approximation by sums of ridge functions with fixed directions”, St. Petersburg Math. J., 28:6 (2017), 741–772
N. J. Guliyev, V. E. Ismailov, “A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function”, Neural Comput., 28:7 (2016), 1289–-1304
V. E. Ismailov, “On the approximation by neural networks with bounded number of neurons in hidden layers”, J. Math. Anal. Appl., 417:2 (2014), 963–969
V. E. Ismailov, A. Pinkus, “Interpolation on lines by ridge functions”, J. Approx. Theory, 175 (2013), 91–113
V. E. Ismailov, “Approximation by neural networks with weights varying on a finite set of directions”, J. Math. Anal. Appl., 389:1 (2012), 72–83
V. E. Ismailov, “On the theorem of M Golomb”, Proc. Indian Acad. Sci. Math. Sci., 119:1 (2009), 45–52
V. E. Ismailov, “On the representation by linear superpositions”, J. Approx. Theory, 151:2 (2008), 113–125
