Publications
 

The papers in the list are arranged subjectwise and antichronologically within a subject.

 

Chaotic linear dynamics

S.Shkarin,  A weighted bilateral shift with cyclic square is supercyclic,  Bull. London Math. Soc. [to appear]

S.Shkarin,  Kitai Criterion and backward weighted shifts,  Proc. Amer. Math. Soc. [to appear]

A.Montes-Rodriguez and S.Shkarin,  Non-weakly supercyclic operators, J. Operator Theory 58 (2007), 39-62

S.Shkarin,  Non-sequential weak supercyclicity and hypercyclicity, J. Funct. Anal. 242 (2007), 37-77

S.Shkarin,  Antisupercyclic operators and orbits of the Volterra operator,  J. Lond. Math. Soc. 73 (2006), 506-528

S.Shkarin,  On the growth of D-universal functions,  Moscow Univ. Math. Bull.  48 (1993), 49-51 

 

Infinite dimensional analysis 

S.Shakrin,  Compact perturbations of linear differential equations in locally convex spaces,  Studia Mathematica 172 (2006), 203-22

S.Shkarin, On solvability of linear differential equations in $R^N$,  Demonstratio Math. 38 (2005), 85-99

A.Leonov and S.Shkarin,  On weak and strong Peano theorems, Russ. J. Math. Phys. 11 (2004), 77-80 

S.Shkarin and O.Smolyanov,  Complex Gateaux differentiability and continuity,  Izv. Math. 68 (2004), 1217-1227

S.Shkarin,  On Osgood theorem in Banach spaces,  Math. Nachr. 257 (2003), 87-98 

S.Shkarin,  Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces, Demonstratio Math. 36 (2003), 611-626

S.Shkarin,  On solvability of Hamilton's equations in Hilbert spaces,  Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (2003) 145-154 

A.Leonov and S.Shkarin,  Integral completeness of locally convex spaces,   Russ. J.  Math. Phys. 7 (2000), 402-412

S.A.Shkarin,  Whitney's type theorems for infinite dimensional spaces,  Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (2000), 141-160

S.Shkarin,  Extending smooth functions from linear subspaces of locally convex spaces,  Journal Math. Sci. (New York) 91 (1998), 3323-3338

S.Shkarin,  Counter-example to Peano's theorem in infinite dimensional F'-spaces,  Math.  Notes 62 (1997), 108-115 

S.Shkarin,   Peano's theorem in infinite-dimensional Frechet spaces is invalid,  Functional Anal. Appl. 27 (1993), 149-151

S.Shkarin,  Points of discontinuity of Gateaux-differentiable mappings,  Siberian Math. J. 33 (1992), 905-913

S.Shkarin,  On Rolle's theorem in infinite-dimensional Banach spaces,  Math. Notes  51 (1992), 311-317

S.Shkarin,  Some results on solvability of ordinary linear equationsin locally convex spaces,  Math. USSR Sbornik  71 (1992), 29-40

V.Bogachev and S.Shkarin,  Differentiable and Lipschitz mappings of Banach spaces,  Math. Notes 44 (1988), 790-798

 

Nonlinear chaotic dynamical systems
 

I.Antoniou, K.Gustafson and S.Shkarin,  Positive dilations of piecewise monotonic Markov maps,  Infin. Dimens. Anal. Quantum Probab. Relat. Top.  7 (2004), 261-269

S.Shkarin and O.Smolyanov,  Time operators of one-parametric semigroups,  Russ. J. Math. Phys. 10 (2003), 473-486

I.Antoniou and S.Shkarin,  Resonances and time operator of the cusp map,  Chaos Solitons Fractals 17 (2003), 445-448 

I.Antoniou and S.Shkarin,  Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map,  J. Stat. Phys. 111 (2003), 355-369

I.Antoniou, S.Shkarin and E.Yarevsky,  The resonance spectrum of the cusp map in the space of analytic functions,  J. Math. Phys. 43 (2002), 3746-3758

I.Antoniou, S.Shkarin and E.Yarevsky,  Resonances of the cusp family,  J. Phys. A35 (2002), 2833-2844

I.Antoniou, I.Prigogine, V.Sadovnichii and S.Shkarin,  Time operator for diffusion,  Chaos, Solitons and Fractals 11 (2000), 465-477 

I.Antoniou, Yu.Melnikov, S.Shkarin and Z.Suchanetcki,  Extended spectral decompositions of the Renyi map,  Chaos, Solitons and Fractals 11 (2000), 393-421 

I.Antoniou, V.Sadovnichii and S.Shkarin,  Time operators and shift representation of dynamical systems,  Physica A269 (1999), 299-313

I.Antoniou, V.Sadovnichii and S.Shkarin,  New extended spectral decompositions of the Renyi map,  Phys. Lett. A 258 (1999), 237-243

I.Antoniou, S.Shkarin and Z.Suchanetcki,  The spectrum of the Liouville-von Newmann operator in the Hilbert-Schmidt space, Journal of Math. Phys.  40 (1999), 4106-4118

I.Antoniou and S.Shkarin,  Extended spectral decompositions of evolution operators,  Research Notes in Mathematics 399, Generalized Functions, Operator Theory and Dynamical Systems, 171-201, Chapman
and Hall, Boca Raton, 1999


Infinite dimensional topology

S.Shkarin,  Embedding of finite ultrametric spaces in Banach spaces, Topology Appl. 142 (2004), 13-17

S.Shkarin,  Monotonically normal topological vector spaces are stratifiable,  Topology Appl. 136 (2003), 129-134

E.Reznichenko and S.Shkarin,  On linear extension operators, Russ. J. Math. Phys. 9 (2002), 188-197

S.Shkarin,  Three constructive examples of pre-Hilbert spaces non-isomorphic to their closed hyperplanes,  Russ. J. Math. Phys. 8 (2001), 106-121

M.Matveev and S.Shkarin,  Some questions on topological homogeneity, Questions Answers Gen. Topology 18 (2000), 1-16

S.Shkarin,  Q-universal normed groups,  Moscow Univ. Math. Bull. 55 (2000), 45-47

S.Shkarin,  An infinite-dimensional pre-Hilbert space that is non-homeomorphic to its closed hyperplane,  Izv. Math. 63 (2000),  1263-1273

S.Shkarin,  On stratifiable  locally convex spaces,  Russ. J. Math. Phys. 6 (1999), 435-460

S.Shkarin,  On universal abelian topological groups,  Sbornik Math. 190 (1999), 1059-1076


General operator theory 

S.Shkarin,  Compact operators without extended eigenvalues,  J. Math. Anal. Appl.  332 (2007), 455-462

S.Shkarin,  On similarity of quasinilpotent operators,  J. Funct. Anal. 241 (2006), no. 2, 528-556  

A.Montes-Rodriguez and S.Shakrin,  New results on a classical operator,  Contemp. Math. 393 (2006), 139-158

S.Shkarin and O.Smolyanov,  On spectral structure of bounded linear operators on reflexive Banach spaces,  Proceedings of the First Advanced Course in Operator Theory and Complex Analysis, 133-146,
Univ. Sevilla Secr. Publ., Seville, 2006

S.Shkarin,  Continuous restrictions of linear operators,  Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4 (2001), 121-132

S.Shkarin and O.Smolyanov,  On the structure of spectra of linear operators in Banach spaces,  Sbornik Math. 192 (2001), 577-591

S.Shkarin,  On the spectra of continuous linear operators on separable Fr'echet spaces,  Math.  Notes 69 (2001), 587-590
 

Miscellaneous  

L.Frerick and S.Shkarin,  Completeness of certain function spaces, Bull. Belg. Math. Soc.  14 (2007), 509-512 

Yu.Kuznetsova and S.Shkain,  Multiplicative spectra of Banach spaces,  J. Math. Sci. (New York) 131 (2005), 6112-6119

I.Antoniou and S.Shkarin,  Decay Spectrum and decay subspace of normal operators,  Proc.  Roy. Soc. Edinburgh A131 (2001), 1245-1256

I.Antoniou and S.Shkarin,  Decay Measures on locally compact abelian topological groups,  Proc. Roy. Soc. Edinburgh A131 (2001), 1257-1274

S.Shkarin,  On effective linearly ordered sets of comparison functions,   Math. Notes 67 (2000), 534-540

I.Antoniou and S.Shkarin,  Decomposition of singular measures, Dokl. Math. 61 (2000), 24-27

S.Shkarin,  On the Gelfand-Dikii method for computing the first eigenvalues of the Sturm-Liouville operator,  Moscow Univ. Math. Bull. 51 (1996) 34-38

Yu.Kuznetsov, S.Shkarin and V.Yaschenko,  On partitions of binary cube, related to one cryptographic problem  (in Russian), Discrete Anal. 2 (1995), 75-86

S.Shkarin,  A class of continuous nowhere-differentiable functions, Izv. Math.  45 (1995), 423-432

S.Shkarin,  The moment problem in Frechet spaces,  Math. Notes 54 (1993), 739-746

E.Kurmakaeva and S.Shkarin,  On the projectivity of some modules over polynormed algebras of continuous functions,  Moscow Univ. Math. Bull.  45 (1990), 52-53