spectral theory of operators,
self-similar functions.
UDC:
517.984, 517.518
Subject:
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.
Biography
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.
I.A. Sheipak, “Netrivialnye fraktaly na ploskosti i lineinye operatory s sovmestnym spektralnym radiusom edinitsa”, Matematicheskie zametki, 63:5 (1998), 797–800
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
T. A. Garmanova, I. A. Sheipak, “Exact estimates for higher order derivatives in Sobolev spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 1, 3–10; Moscow University Mathematics Bulletin, 79:1 (2024), 1–10
I. A. Sheipak, “Bernoulli numbers in the embedding constants of Sobolev spaces with different boundary conditions”, Algebra i Analiz, 35:2 (2023), 226–245; St. Petersburg Math. J., 35:2 (2024), 417–431
3.
T. A. Garmanova, I. A. Sheipak, “Relationship Between the Best $L_p$ Approximations of Splines by Polynomials with Estimates of the Values of Intermediate Derivatives in Sobolev Spaces”, Mat. Zametki, 114:4 (2023), 623–627; Math. Notes, 114:4 (2023), 625–629
I. A. Sheipak, “Chebyshev-Type Polynomials Arising in Poincaré Limit Inequalities”, Mat. Zametki, 112:1 (2022), 153–157; Math. Notes, 112:1 (2022), 163–167
2021
5.
E. B. Sharov, I. A. Sheipak, “String equation with weight that is a noncompact multiplier: continuous spectrum and eigenvalues”, Algebra i Analiz, 33:4 (2021), 155–172; St. Petersburg Math. J., 33:4 (2022), 697–709
6.
T. A. Garmanova, I. A. Sheipak, “On Sharp Estimates of Even-Order Derivatives in Sobolev Spaces”, Funktsional. Anal. i Prilozhen., 55:1 (2021), 43–55; Funct. Anal. Appl., 55:1 (2021), 34–44
T. A. Garmanova, I. A. Sheipak, “Orthogonality Relations for the Primitives of Legendre Polynomials and Their Applications to Some Spectral Problems for Differential Operators”, Mat. Zametki, 110:4 (2021), 498–506; Math. Notes, 110:4 (2021), 489–496
I. A. Sheipak, “On Hölder exponents of the self-similar functions”, Funktsional. Anal. i Prilozhen., 53:1 (2019), 67–78
9.
I. A. Sheipak, T. A. Garmanova, “An explicit form for extremal functions in the embedding constant problem for Sobolev spaces”, Tr. Mosk. Mat. Obs., 80:2 (2019), 221–246; Trans. Moscow Math. Soc., 80 (2019), 189–210
J. V. Tikhonov, S. V. Shaposhnikov, I. A. Sheipak, “On the Singularity of Functions and the Quantization of Probability Measures”, Mat. Zametki, 102:4 (2017), 628–631; Math. Notes, 102:4 (2017), 587–590
2016
11.
J. V. Tikhonov, I. A. Sheipak, “On the string equation with a singular weight belonging to the space
of multipliers in Sobolev spaces with negative index of smoothness”, Izv. RAN. Ser. Mat., 80:6 (2016), 258–273; Izv. Math., 80:6 (2016), 1242–1256
J. V. Tikhanov, I. A. Sheipak, “Description of Self-Similar Multipliers in Negative Sobolev Spaces Satisfying the Dirichlet Condition”, Mat. Zametki, 99:2 (2016), 314–318; Math. Notes, 99:2 (2016), 335–339
2015
13.
I. A. Sheipak, “Asymptotics of the Spectrum of a Differential Operator with the Weight Generated by the Minkowski Function”, Mat. Zametki, 97:2 (2015), 302–308; Math. Notes, 97:2 (2015), 289–294
A. A. Vladimirov, I. A. Sheipak, “On the Neumann Problem for the Sturm–Liouville Equation with Cantor-Type Self-Similar Weight”, Funktsional. Anal. i Prilozhen., 47:4 (2013), 18–29; Funct. Anal. Appl., 47:4 (2013), 261–270
A. A. Vladimirov, I. A. Shejpak, “Eigenvalue asymptotics of the problem of high odd order with dicrete self-similar weight”, Algebra i Analiz, 24:2 (2012), 104–119; St. Petersburg Math. J., 24:2 (2013), 263–273
N. V. Gaganov, I. A. Sheipak, “A boundedness criterion for the variations of self-similar functions”, Sibirsk. Mat. Zh., 53:1 (2012), 68–88; Siberian Math. J., 53:1 (2012), 55–71
A. A. Vladimirov, I. A. Sheipak, “Asymptotics of the Eigenvalues of the Sturm–Liouville Problem with Discrete Self-Similar Weight”, Mat. Zametki, 88:5 (2010), 662–672; Math. Notes, 88:5 (2010), 637–646
I. A. Sheipak, “Singular points of a self-similar function of spectral order zero: self-similar Stieltjes string”, Mat. Zametki, 88:2 (2010), 303–316; Math. Notes, 88:2 (2010), 275–286
I. A. Sheipak, “On the Construction and Some Properties of Self-Similar Functions in the Spaces $L_p[0,1]$”, Mat. Zametki, 81:6 (2007), 924–938; Math. Notes, 81:6 (2007), 827–839
A. A. Vladimirov, I. A. Sheipak, “Self-similar functions in $L_2[0,1]$ and the
Sturm–Liouville problem with singular indefinite weight”, Mat. Sb., 197:11 (2006), 13–30; Sb. Math., 197:11 (2006), 1569–1586
A. A. Vladimirov, I. A. Sheipak, “Indefinite Sturm–Liouville Problem for Some Classes of Self-similar Singular Weights”, Trudy Mat. Inst. Steklova, 255 (2006), 88–98; Proc. Steklov Inst. Math., 255 (2006), 82–91
A. A. Vladimirov, I. A. Sheipak, “Spectral properties of a certain operator matrix”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2004, no. 3, 23–30
2001
24.
I. A. Sheipak, “Spectral problems associated with stability of fluid motion in an annulus in a magnetic field”, Fundam. Prikl. Mat., 7:2 (2001), 583–596
1998
25.
I. A. Sheipak, “Nontrivial fractals in the plane and linear operators with joint spectral radius equal to 1”, Mat. Zametki, 63:5 (1998), 797–800; Math. Notes, 63:5 (1998), 701–705
I. A. Sheipak, “The eigenfunction system of a hydrodynamical problem is a Riesz basis”, Mat. Zametki, 58:5 (1995), 790–793; Math. Notes, 58:5 (1995), 1238–1241
27.
I. A. Sheipak, “On the basis properties of systems of root vectors of operators that are almost self-adjoint in Pontryagin spaces”, Mat. Zametki, 57:6 (1995), 937–940; Math. Notes, 57:6 (1995), 665–667
28.
I. A. Sheipak, “Spectral analysis of asymmetric disturbed Couette flow and related problems of hydrodynamic stability”, Mat. Zametki, 57:2 (1995), 278–282; Math. Notes, 57:2 (1995), 194–197
2019
29.
A. I. Aptekarev, A. M. Akhtyamov, O. V. Besov, A. A. Vladimirov, B. S. Kashin, K. A. Mirzoev, S. N. Naboko, R. O. Oinarov, I. V. Sadovnichaya, A. M. Savchuk, A. G. Sergeev, V. D. Stepanov, Ya. T. Sultanaev, D. V. Treschev, I. A. Sheipak, “Andrei Andreevich Shkalikov (on his seventieth birthday)”, Tr. Mosk. Mat. Obs., 80:2 (2019), 133–145; Trans. Moscow Math. Soc., 80 (2019), 113–122
2018
30.
B. A. Budak, D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, “Олимпиада «Ломоносов»-2018. Математика”, Kvant, 2018, no. 11, 54–55
2017
31.
D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, L. V. Kritskov, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, M. V. Yumashev, “Олимпиада «Покори Воробьевы горы!»”, Kvant, 2017, no. 9, 53–55
32.
D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, L. V. Kritskov, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, M. V. Yumashev, S. S. Chesnokov, “Олимпиада «Ломоносов»-2017”, Kvant, 2017, no. 4, 52–58
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