Showing papers in "Mathematics of The Ussr-izvestiya in 1973"
TL;DR: In this paper, a degenerate Hamiltonian system arbitrarily close in the topology to a given integrable degenerate system of class which generates an ergodic flow on each manifold of constant energy is constructed.
Abstract: Hamiltonian systems arbitrarily close in the topology to a given integrable degenerate Hamiltonian system of class which generate an ergodic flow on each manifold of constant energy are constructed. Applications: Small perturbations of a system generated by independent oscillators and Finsler metrics close to standard Riemannian metrics on symmetric spaces of rank 1.
201 citations
TL;DR: In this paper, the quiver representations are described, which do not contain the problem of reducing a pair of matrices by similarity transformations, and do not suffer from the same problem as our quiver representation.
Abstract: In this paper we describe the quiver representations (see Manuscripta Math. 6(1972), 71-103) which do not contain the problem of reducing a pair of matrices by similarity transformations.
190 citations
TL;DR: In this paper, a system of caustics is found for a plane convex domain with a sufficiently smooth boundary; the Caustics are close to the boundary and occupy a set of positive measure.
Abstract: A system of caustics is found for a plane convex domain with a sufficiently smooth boundary; the caustics are close to the boundary and occupy a set of positive measure. A caustic is a convex smooth curve lying in the domain and possessing the property that a tangent to it becomes another tangent to the same curve after reflection from the boundary according to the law of geometrical optics.
184 citations
TL;DR: In this article, a direct topological-geometric method is proposed for constructing solutions of partial differential inequalities and equations. But the method is not suitable for the case of complex problems.
Abstract: A direct topological-geometric method is suggested for constructing solutions of partial differential inequalities and equations.
133 citations
TL;DR: For any natural number n, the authors constructed an associative multilinear polynomial whose values on matrices of order n are scalar matrices at least one of which is nonzero.
Abstract: In this article we construct for any natural number n an associative multilinear polynomial whose values on matrices of order n are scalar matrices at least one of which is nonzero.
85 citations
TL;DR: In this paper, the notion of a Markov system of processes is introduced, and it is proved that an arbitrary Markov process can be selected from such a system by constructing quasidiffusion processes with "poor" coefficients (e.g. with a degenerate diffusion matrix).
Abstract: In this paper the notion of a Markov system of processes is introduced, and it is proved that a Markov process can be selected from such a system. The usefulness of this fact is illustrated by the example of constructing quasidiffusion processes with "poor" coefficients (e.g. with a degenerate diffusion matrix).
78 citations
TL;DR: In this paper, the authors give conditions under which the completion of the kernel of a homomorphism of analytic rings coincides with the kernel kernel of the corresponding homomorphisms of the completions.
Abstract: In this paper we give conditions under which the completion of the kernel of a homomorphism of analytic rings coincides with the kernel of the corresponding homomorphism of the completions .
75 citations
TL;DR: In this article, the authors examined the extremal problem of finding the quantity where is an -dimensional sphere and is the totality of polynomials of degree in variables for which the first sup is taken over all measurable having measure.
Abstract: This article is devoted to an examination of the following extremal problem: find the quantity where is an -dimensional sphere and is the totality of polynomials of degree in variables for which . Here is a measurable set from and the first sup is taken over all measurable having measure . The exact order of growth of which respect to as is found in this article. Various applications of the results are examined as well.
70 citations
TL;DR: In this paper, the authors classify up to G-isomorphism all normal affine irreducible quasihomogeneous (i.e. containing a dense orbit) varieties of the group G = SL(2) which are defined over an algebraically closed field of characteristic zero.
Abstract: We classify up to G-isomorphism all normal affine irreducible quasihomogeneous (i.e. containing a dense orbit) varieties of the group G = SL(2) which are defined over an algebraically closed field of characteristic zero.
57 citations
TL;DR: For matrix-valued functions of Schur class (holomorphic and contractive in the circle ) the author considers the Darlington realization and isolates the set of those for which this realization is possible.
Abstract: For matrix-valued functions of Schur class (holomorphic and contractive in the circle ) the author considers the Darlington realization and isolates the set of those for which this realization is possible. For the case in which satisfies the condition 0$ SRC=http://ej.iop.org/images/0025-5726/7/6/A06/tex_im_2088_img5.gif/>, a description is obtained of all Darlington realizations of and the minimum realizations are isolated.
48 citations
TL;DR: In this paper, it was shown that the title equation with continuous and even analytic right-hand side may have a measurable solution which is not Lebesgue integrable (and even with "worse" properties).
Abstract: It is shown that the title equation with continuous and even analytic right-hand side may have a measurable solution which is not Lebesgue integrable (and even with "worse" properties).Bibliography: 13 titles.
TL;DR: In this paper, necessary and sufficient conditions for continuity, compactness, and closability of imbedding operators of some function spaces into the space Lp are given. But they do not consider differentiable functions on a cube.
Abstract: Necessary and sufficient conditions are found for continuity, compactness, and closability of imbedding operators of some function spaces into the space Lp. These results (for p = 2) give criteria for positive definiteness and discreteness of the spectrum of the Dirichlet problem for a selfadjoint elliptic operator of arbitrary order. Some integral inequalities are considered for differentiable functions on a cube.
TL;DR: In this paper, it was shown that a semisimple -ring has a finite number of indecomposable integral representations if and only if it is a hereditary ring, has two generators as a -module, and is cyclic.
Abstract: Let be a semisimple -ring and its center. Assume that for any prime ideal the ring is primary. Let be the intersection of the maximal over-rings of , and . We prove that has a finite number of indecomposable integral representations if and only if is a hereditary ring, has two generators as a -module, and is cyclic.
TL;DR: In this paper, the authors studied the relation between invariants of a knot of codimension 2 and coverings of the ball branched over orientable compact submanifolds spanning ; analogous relationships are studied in a more general situation.
Abstract: In this paper relationships are found between invariants of a knot of codimension 2 and invariants of cyclic branched coverings of the ball branched over orientable compact submanifolds spanning ; analogous relationships are studied in a more general situation.Bibliography: 10 titles.
TL;DR: A general method for proving that certain T-ideals are Spechtian is given in this article, where it is shown that the Tideal is a special case of the T-approximation.
Abstract: A general method is given for proving that certain T-ideals are Spechtian. In particular, the T-ideal is shown to be Spechtian.
TL;DR: In this paper, a simplified upper bound which is uniform in all parameters for the mean value of the modulus of a trigonometric sum is obtained. But this upper bound is not applicable to the case of the trigonometrical sum.
Abstract: We obtain a simplified upper bound which is uniform in all parameters for the mean value of the modulus of a trigonometric sum.Bibliography: 5 titles
TL;DR: In this article, it was proved that for any finitely based variety of groups there exists a finitely-based left factor such that their product is infinitely based (the left factor is a Burnside variety).
Abstract: It is proved that for any finitely based variety of groups there exists a finitely based left factor such that their product is infinitely based (the left factor is a Burnside variety).
TL;DR: For pseudodifferential operators with a finite group of shifts, this article constructed a theory analogous to the theory of elliptic pseudo-differential operators on a closed manifold, and found conditions under which the operators are Noetherian.
Abstract: For pseudodifferential operators with a finite group of shifts we construct a theory analogous to the theory of elliptic pseudodifferential operators on a closed manifold. We will find conditions under which the operators are Noetherian, and we will obtain a formula for the index.
TL;DR: In this paper, a complete solution to the problem of Zygmund on the absolute convergence of the Fourier series of a function of bounded variation is given, which is the same problem as ours.
Abstract: In this paper a complete solution is given to a problem of Zygmund on the absolute convergence of the Fourier series of a function of bounded variation.Bibliography: 8 items.
TL;DR: In this article, the authors studied Hilbert space operators which are dissipative with respect to a continuous Hermitian-bilinear form, and showed that these operators can be dissipated by Hermitians.
Abstract: We will study Hilbert space operators which are dissipative with respect to a continuous Hermitian-bilinear form.
TL;DR: In this paper, a system of differential equations on the semiaxis is considered with operator coefficients in a Hilbert space, and the coefficients of the system depend on and for are stabilized in a certain sense.
Abstract: A system of differential equations on the semiaxis is considered with operator coefficients in a Hilbert space. The coefficients of the system depend on and for are stabilized in a certain sense. The spectrum of the limit operator consists of normal eigenvalues and is contained inside a certain double angle with opening less than which contains the imaginary axis. Asymptotic formulas are derived for the solution, and the contribution which a multiple eigenvalue of the limiting operator pencil makes to the asymptotic expressions is investigated.Bibliography: 17 titles.
TL;DR: In this article, the relationship between spectral properties of an th degree polynomial operator bundle and spectral properties for roots of the corresponding operator equation is investigated, based on the concept of Vandermonde operator.
Abstract: The paper treats the relationship between spectral properties of an th degree polynomial operator bundle and spectral properties of roots of the corresponding operator equation. Basic to this investigation is the concept, introduced in this paper, of Vandermonde operator.
TL;DR: In this article, the authors investigated conditions for which all functions of W can be analytically continued to a larger region in the complex plane, where W is a nontrivial invariant subspace in H which admits a spectral synthesis.
Abstract: Let G be a region in the complex plane; let H be the space of functions analytic in G with the topology of uniform convergence on compacta of G; let W be a nontrivial invariant (with respect to differentiation) subspace in H which admits a spectral synthesis. We investigate conditions for which all functions of W can be analytically continued to a larger region .
TL;DR: A method is given for computing the Tate-Safarevic pairing on elliptic curves for simple cyclic extensions and the properties of this pairing are investigated over both a local field and a general local field of definition.
Abstract: In this paper a method is given for computing the Tate-Safarevic pairing on elliptic curves for simple cyclic extensions. With this foundation the properties of the Tate-Safarevic pairing are investigated over both a local field and a general local field of definition.Bibliography: 28 titles.
TL;DR: In this article, it was shown that the regularity problem has an affirmative solution in the two-dimensional case, in particular in the case of a quasilinear elliptic equation of divergent type.
Abstract: Regularity is proved for an arbitrary generalized solution of a quasilinear elliptic equation of divergent type which belongs to , for an arbitrary strictly interior subregion of a region ( is the order of the equation, and is the number of arguments). It follows from this, in particular, that the regularity problem has an affirmative solution in the two-dimensional case.Bibliography: 21 titles.
TL;DR: In this paper, the notion of the zeta function is generalized to rings which are orders in classical Dedekind rings, and the structure of these functions is explained for which the classical assertions (the Riemann hypothesis, functional equation) are applicable.
Abstract: The notion of the zeta-function is generalized to rings which are orders in classical Dedekind rings; the structure of these functions is explained. Classes of rings are given for which the classical assertions (the Riemann hypothesis, functional equation) are applicable.
TL;DR: In this paper, it was shown that the spectral functions of the second-order boundary value problem possess power asymptotics as, when the function possesses power-asymptotic as, and a partial converse of this fact was also obtained.
Abstract: It is established that the spectral functions of the second-order boundary value problem possess power asymptotics as , when the function possesses power asymptotics as . A partial converse of this fact is also obtained.
TL;DR: In this article, it was shown that the complement in the space of all germs of analytic mappings from Cn to Cq of the set of germs whose topological type is unchanged under alteration of large terms of the Taylor series has infinite codimension.
Abstract: In this paper one studies the local topological structure of analytic mappings. It is proved that the complement in the space of all germs of analytic mappings from Cn to Cq of the set of germs whose topological type is unchanged under alteration of large terms of the Taylor series has infinite codimension.
TL;DR: In this article, it was shown that Z is the field of fractions of the center of R and that the transcendence degree of Z over F is equal to the maximal length of a chain of prime ideals in R.
Abstract: Let R be a finitely generated prime Pl-algebra over a field F. Z is the center of its ring of fractions. It is proved that Z is the field of fractions of the center of R and that the transcendence degree of Z over F is equal to the maximal length of a chain of prime ideals in R.
TL;DR: In this article, all affine algebraic surfaces that admit a quasitransitive algebraic group of biregular automorphisms (i.e., a group such that the complement of one orbit of the action is either empty or of dimension zero) are studied.
Abstract: We find all the affine algebraic surfaces that admit a quasitransitive algebraic group of biregular automorphisms (i.e. a group such that the complement of one orbit of the action is either empty or of dimension zero). The ground field is algebraically closed and of characteristic zero.