Ikromov Isroil Akramovich

Professor | Doctor of Physical and Mathematical Sciences, Professor

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Introduction to Harmonic Analysis, Theory of Distributions

 

 

In 2017 received the “Simon professorship” award

 

 

1979-1982 - Student at Samarkand State University
1982-1985 - Student at Moscow State University
1985-1985 - Research intern at the Institute of Mathematics of the Academy of Sciences of Uzbekistan
1985-1988 - PhD student at Moscow State University
1988-1991 - Assistant of the Department of “Functional Analysis” of Samarkand State University
1991-1994 - Doctoral student at Tashkent State University
1994-2001 - Senior researcher at the Samarkand branch of the Academy of Sciences of Uzbekistan
2001-2021 - Head of the Department of Mathematical Analysis, Samarkand State University
2021 - present - Professor of the Department of Mathematical Analysis, Samarkand State University

 

 

Theory of asymptotics and singularities of oscillating integrals and their applications, in particular maximal operators and obtaining smooth estimates for Fur'e transformations. This is called the problem of boundedness of maximal operators I.M. Stein in Lebesgue spaces associated with hypersurfaces in Euclidean space. These operators are studied mainly in the case of convex surfaces (of finite order). The problem of the limitation of such operators is considered one of the pressing problems of modern analysis. Many scientists from all over the world were engaged in scientific work in this area, for example, American mathematicians I. Stein, K. Soji, A. Greenleaf, A. Seeger, A. Ioshevich, Italian mathematicians F. Ricci, G. Mauceri and others. In collaboration with German scientists D. Muller and M. Kempe, I. Ikramov gave a complete solution to the problem of the boundedness of maximal operators with the Lebesgue index r>2 for smooth hypersurfaces in three-dimensional space. From their scientific results, in particular, a solution to one of I’s conjectures was derived. Stein (her confirmation). The famous American scientist I. Stein stated this in 2008 at a conference in Oberwolfach in Germany. These results were published in the journal Mathematical Sciences. In recent years, it has become a tradition to create various algorithms for calculating algorithms for many mathematical problems on modern computers. In particular, new modern departments called computer algebra have appeared. The normalization of functions specified by the classification theorems of W. Arnold, which caused great resonance in the 80s, is still carried out today through a program called “singular”.

 

 

"1. (Q1) Stefan Buschenhenke Isroil A. Ikromov Detlef Müller The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze conjecture and its proof for generic 2-surfaces
https://doi.org/10.2422/2036-2145.202301_016 2.(Q3)Ikromov I.A., Barakayev A.M., Russian Mathematics, 2023, Vol. 67, No. 7, pp. 17–26.
3.(Q3)Isroil A. Ikromov, Akbar R. Safarov, Akmal T. Absalamov, Journal of Siberian Federal University. Mathematics & Physics 2023, 16(4), 1–10.
4.Jean-Claude Cuenin, Isroil A Ikromov. Sharp time decay estimates for the discrete Klein–Gordon equation,Nonlinearity,2021/10/1410.https://iopscience.iop.org/article/10.1088/1361-6544/ac2b86
5.IA Ikromov, SE Usmanov,On boundedness of maximal operators associated with hypersurfaces,Journal of Mathematical Sciences, Vol. 264, No. 6, July, 2022
6.Isroil Akramovich Ikromov, Dildora Ikromova,Sharp -Estimates for the Fourier Transform of Surface Measures,Russian Academy of Sciences, Steklov Mathematical Institute of Russian Academy of Sciences,2024, 51-77"