Sheipak Igor Anatolievich

Statistics Math-Net.Ru
Total publications: 17
Scientific articles: 17
Presentations: 4

Number of views:
This page:2062
Abstract pages:5181
Full texts:917
Associate professor
Candidate of physico-mathematical sciences (1995)
Birth date: 7.01.1967
Phone: +7 (495) 939 55 40
Fax: +7 (495) 939 55 40
E-mail: ,
Keywords: spectral theory of operators, self-similar functions.
UDC: 517.984, 517.518


The operator model for flow of viscouse fluid between two coaxial cilinders is considered. Asymptotic of spectrum is obtained. Eigenfunctions of corresponding linear pencil form Bari basis in special Hilbert space. The operator model for flow of non-viscouse fluid between two coaxial cilinders is considered. The structure of spectrum is investigated. There are an interval of essential spectrum. The problem of accumulation of eigenvalues to bounds of essential spectrum is studied.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1991 (department of theory of functions and functional analysis). Ph. D. thesis was defended in 1995.

Main publications:
  1. I.A. Sheipak, “Spektralnyi analiz zadach, svyazannykh s nesimmetrichno-vozmuschennym techeniem Kuetta”, Matematicheskie zametki, 57:2 (1995), 278–282  mathnet  mathscinet  zmath
  2. I.A. Sheipak, “Netrivialnye fraktaly na ploskosti i lineinye operatory s sovmestnym spektralnym radiusom edinitsa”, Matematicheskie zametki, 63:5 (1998), 797–800  mathnet  mathscinet  zmath
  3. I.A. Sheipak, “K teorii ustoichivosti dvizheniya zhidkosti v koltsevom kanale v prisutstvii magnitnogo polya i svyazannye spektralnye zadach”, Fundamentalnaya i prikladnaya matematika, 7:2 (2001), 583–596  mathnet  mathscinet  zmath
  4. A.A. Vladimirov, I.A. Sheipak, “Indefinitnaya zadacha Shturma-Liuvillya dlya nekotorykh klassov samopodobnykh singulyarnykh vesov”, Trudy MIAN, 255, 206, 88–98  mathnet  mathscinet
  5. I.A. Sheipak, “O konstruktsii i nekotorykh svoistvakh samopodobnykh funktsii v prostranstvakh $L_2[0,1]$”, Matematicheskie zametki, 81:6 (2007), 924–938  mathnet  mathscinet  zmath
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. On the Singularity of Functions and the Quantization of Probability Measures
J. V. Tikhonov, S. V. Shaposhnikov, I. A. Sheipak
Mat. Zametki, 102:4 (2017),  628–631
2. On the string equation with a singular weight belonging to the space of multipliers in Sobolev spaces with negative index of smoothness
J. V. Tikhonov, I. A. Sheipak
Izv. RAN. Ser. Mat., 80:6 (2016),  258–273
3. Description of Self-Similar Multipliers in Negative Sobolev Spaces Satisfying the Dirichlet Condition
J. V. Tikhanov, I. A. Sheipak
Mat. Zametki, 99:2 (2016),  314–318
4. Asymptotics of the Spectrum of a Differential Operator with the Weight Generated by the Minkowski Function
I. A. Sheipak
Mat. Zametki, 97:2 (2015),  302–308
5. On the Neumann Problem for the Sturm–Liouville Equation with Cantor-Type Self-Similar Weight
A. A. Vladimirov, I. A. Sheipak
Funktsional. Anal. i Prilozhen., 47:4 (2013),  18–29
6. Eigenvalue asymptotics of the problem of high odd order with dicrete self-similar weight
A. A. Vladimirov, I. A. Shejpak
Algebra i Analiz, 24:2 (2012),  104–119
7. A boundedness criterion for the variations of self-similar functions
N. V. Gaganov, I. A. Sheipak
Sibirsk. Mat. Zh., 53:1 (2012),  68–88
8. Asymptotics of the Eigenvalues of the Sturm–Liouville Problem with Discrete Self-Similar Weight
A. A. Vladimirov, I. A. Sheipak
Mat. Zametki, 88:5 (2010),  662–672
9. Singular points of a self-similar function of spectral order zero: self-similar Stieltjes string
I. A. Sheipak
Mat. Zametki, 88:2 (2010),  303–316
10. On the Construction and Some Properties of Self-Similar Functions in the Spaces $L_p[0,1]$
I. A. Sheipak
Mat. Zametki, 81:6 (2007),  924–938
11. Self-similar functions in $L_2[0,1]$ and the Sturm–Liouville problem with singular indefinite weight
A. A. Vladimirov, I. A. Sheipak
Mat. Sb., 197:11 (2006),  13–30
12. Indefinite Sturm–Liouville Problem for Some Classes of Self-similar Singular Weights
A. A. Vladimirov, I. A. Sheipak
Tr. Mat. Inst. Steklova, 255 (2006),  88–98
13. Spectral problems associated with stability of fluid motion in an annulus in a magnetic field
I. A. Sheipak
Fundam. Prikl. Mat., 7:2 (2001),  583–596
14. Nontrivial fractals in the plane and linear operators with joint spectral radius equal to 1
I. A. Sheipak
Mat. Zametki, 63:5 (1998),  797–800
15. The eigenfunction system of a hydrodynamical problem is a Riesz basis
I. A. Sheipak
Mat. Zametki, 58:5 (1995),  790–793
16. On the basis properties of systems of root vectors of operators that are almost self-adjoint in Pontryagin spaces
I. A. Sheipak
Mat. Zametki, 57:6 (1995),  937–940
17. Spectral analysis of asymmetric disturbed Couette flow and related problems of hydrodynamic stability
I. A. Sheipak
Mat. Zametki, 57:2 (1995),  278–282

Presentations in Math-Net.Ru
1. Об асимптотике спектра задачи с весом, порожденным функцией Минковского
I. A. Sheipak
Differential equations, analysis and control: theory and applications
April 2, 2018 18:25
2. Дискретный и непрерывный спектр в задаче о колебаниях струны Крейна
I. A. Sheipak
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
February 28, 2018 16:00   
3. О спектре задачи Штурма–Лиувилля с весом-мультипликатором из пространства Соболева с отрицательным индексом гладкости
I. A. Sheipak, J. V. Tikhanov
International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 28, 2015 16:40
4. Оператор Штурма–Лиувилля с самоподобным сингулярным весом
I. A. Sheipak
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
February 24, 2010 16:00

Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018