Том 58, № 2 (2017)
- Год: 2017
- Статей: 18
- URL: https://journals.rcsi.science/0037-4466/issue/view/10413
Article
Differences of idempotents in C*-algebras
Аннотация
Suppose that P and Q are idempotents on a Hilbert space H, while Q = Q* and I is the identity operator in H. If U = P − Q is an isometry then U = U* is unitary and Q = I − P. We establish a double inequality for the infimum and the supremum of P and Q in H and P − Q. Applications of this inequality are obtained to the characterization of a trace and ideal F-pseudonorms on a W*-algebra. Let φ be a trace on the unital C*-algebra A and let tripotents P and Q belong to A. If P − Q belongs to the domain of definition of φ then φ(P − Q) is a real number. The commutativity of some operators is established.
Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions
Аннотация
We establish sharp estimates for the best approximations of convolution classes by entire functions of exponential type. To obtain these estimates, we propose a new method for testing Nikol’skiĭ-type conditions which is based on kernel periodization with an arbitrarily large period and ensuing passage to the limit. As particular cases, we obtain sharp estimates for approximation of convolution classes with variation diminishing kernels and generalized Bernoulli and Poisson kernels.
On convergence of multiple trigonometric series with monotone coefficients
Аннотация
We study the Pringsheim pointwise convergence of multiple trigonometric series. We obtain a condition on the coefficients of the series that guarantees its Pringsheim convergence and prove the unimprovability of this condition.
On semirings whose simple semimodules are projective
Аннотация
We study the semirings whose simple semimodules are all projective. In particular, we establish that for every semiring S this condition implies the injectivity of all simple S-semimodules and show that, in contrast to the case of rings, the projectivity of all simple semimodules in general is not a left-right symmetric property.
On a Frankl-type problem for a mixed parabolic-hyperbolic equation
Аннотация
We state a new nonlocal boundary value problem for a mixed parabolic-hyperbolic equation. The equation is of the first kind, i.e., the curve on which the equation changes type is not a characteristic. The nonlocal condition involves points in hyperbolic and parabolic parts of the domain. This problem is a generalization of the well-known Frankl-type problems. Unlike other close publications, the hyperbolic part of the domain agrees with a characteristic triangle. We prove unique solvability of this problem in the sense of classical and strong solutions.
The polynomial sub-Riemannian differentiability of some Hölder mappings of Carnot groups
Аннотация
The polynomial sub-Riemannian differentiability is established for the large classes of Hölder mappings in the sub-Riemannian sense, namely, the classes of smooth mappings, their graphs, and the graphs of Lipschitz mappings in the sub-Riemannian sense defined on nilpotent graded groups. We also describe some special bases that carry the sub-Riemannian structure of the preimage to the image.
Integral equations of the third kind with unbounded operators
Аннотация
We consider linear functional equations of the third kind in L2 with arbitrary measurable coefficients and unbounded integral operators with kernels satisfying broad conditions. We propose methods for reducing these equations by linear continuous invertible transformations either to equivalent integral equations of the first kind with nuclear operators or to equivalent integral equations of the second kind with quasidegenerate Carleman kernels. To the integral equations obtained after the reduction, one can apply various exact and approximate methods of solution; in particular, the two approximate methods developed in this article.
On exponential stability of solutions to periodic neutral-type systems
Аннотация
We consider periodic systems of delay equations. Exponential stability conditions for the zero solution are pointed out by using the Lyapunov-Krasovskiĭ functional. We give some estimates that characterize the decay rate of solutions at infinity.
On the supersoluble residual of a product of subnormal supersoluble subgroups
Аннотация
We give a sufficient condition for supersolubility of a finite group that is a product of two subnormal supersoluble subgroups. We prove that the supersoluble residual of such a group is equal to its nilpotent residual. Also we apply these results to finite groups that are a product of two subnormal p-supersoluble subgroups.
On some reducibility and existential interpretability of structures
Аннотация
We prove the embeddability of the structure of Turing degrees into the structure of degrees of existential interpretability. The notion of weakly bounded Turing reducibility (wbT-reducibility) arises in the proof naturally. We demonstrate that this reducibility is situated strictly between the bounded truth-table reducibility and Turing reducibility and differs from the truth-table reducibility.
Estimates for a spectral parameter in elliptic boundary value problems with discontinuous nonlinearities
Аннотация
Under study are the two classes of elliptic spectral problems with homogeneous Dirichlet conditions and discontinuous nonlinearities (the parameter occurs in the nonlinearity multiplicatively). In the former case the nonlinearity is nonnegative and vanishes for the values of the phase variable not exceeding some positive number c; it has linear growth at infinity in the phase variable u and the only discontinuity at u = c. We prove that for every spectral parameter greater than the minimal eigenvalue of the differential part of the equation with the homogeneous Dirichlet condition, the corresponding boundary value problem has a nontrivial strong solution. The corresponding free boundary in this case is of zero measure. A lower estimate for the spectral parameter is established as well. In the latter case the differential part of the equation is formally selfadjoint and the nonlinearity has sublinear growth at infinity. Some upper estimate for the spectral parameter is given in this case.
Universal equivalence of some countably generated partially commutative structures
Аннотация
We study universal theories of partially commutative Lie algebras, partially commutative metabelian Lie algebras, and partially commutative metabelian groups such that their defining graphs are trees with countably many vertices. Also we find universal equivalence criteria for each of these classes of Lie algebras and groups.
Connection between holomorphic vector bundles and cohomology on a Riemann surface and conjugation boundary value problems
Аннотация
This paper studies interconnections between holomorphic vector bundles on compact Riemann surfaces and the solution of the homogeneous conjugation boundary value problem for analytic functions on the one hand, and cohomology and the solution of the inhomogeneous problem on the other. We establish that constructing the general solution to the homogeneous problem with arbitrary coefficients in the boundary conditions is equivalent to classifying holomorphic vector bundles. Solving the inhomogeneous problem is equivalent to checking the solvability of 1-cocycles with coefficients in the sheaf of sections of a bundle; in particular, the solvability conditions in the inhomogeneous problem determine obstructions to the solvability of 1-cocycles, i.e. the first cohomology group. Using this connection, we can apply the methods of boundary value problems to vector bundles. The results enable us to elucidate the role of boundary value problems in the general theory of Riemann surfaces.
Finite groups that are products of two normal supersoluble subgroups
Аннотация
Let P1 be the class of all finite groups that are products of two normal supersoluble subgroups. Let P be the class of all nonsupersoluble P1-groups G such that all proper P1-subgroups of G and nontrivial factor groups of G are supersoluble. We classify the P-groups.
On the asymptotics of the motion of a nonlinear viscous fluid
Аннотация
Under study is the nonstationary problem of the motion of a nonlinear-viscous fluid in the case of low or high viscosity. We establish that the convergence of solutions to the corresponding limit solutions as the viscosity converges to zero or infinity.
Special series in Laguerre polynomials and their approximation properties
Аннотация
We consider special series in the classical Laguerre polynomials coinciding in particular cases with the mixed series associated to Laguerre polynomials, introduced by the author previously, as well as Fourier–Sobolev series in Sobolev orthogonal Laguerre polynomials. We address the questions of uniform convergence of these series on a finite segment of the positive half-axis. We study the approximation properties of partial sums of special series on the positive half-axis, with particular attention paid to estimating their Lebesgue function.
Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones
Аннотация
The Cauchy problem is studied for a multidimensional difference equation in a class of functions defined at the integer points of a rational cone. We give an easy-to-check condition on the coefficients of the characteristic polynomial of the equation sufficient for solvability of the problem. A multidimensional analog of the condition ensuring stability of the Cauchy problem is stated on using the notion of amoeba of an algebraic hypersurface.