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Regular version of the site
Of all publications in the section: 174
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Article
Ayano T., Buchstaber V.M. Functional Analysis and Its Applications. 2017. Vol. 51. No. 3. P. 4-21.

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 is described in terms of the gradient of its sigma function. As an application, solutions of the corresponding families of polynomial dynamical systems in C4 with two polynomial integrals are constructed. These systems were introduced by Buchstaber and Mikhailov on the basis of commuting vector fields on the symmetric square of algebraic curves.

Article
Feigin B. L., Mytafyan G. S. Functional Analysis and Its Applications. 2013. Vol. 47. No. 1. P. 50-61.

The generating function of plane partitions {ai,j} subject to the constraint am,n = 0 is expressed and calculated as the character of an irreducible representation of the quantum toroidal algebra gl1 in the case K = q1 mq2 n.

Article
Rudenko D. Functional Analysis and Its Applications. 2016. Vol. 50. No. 1. P. 66-70.

We prove the strong Suslin reciprocity law conjectured by A. B. Goncharov and describe its corollaries for the theory of scissor congruence of polyhedra in hyperbolic space. The proof is based on the study of Goncharov’s conjectural description of certain rational motivic cohomology groups of a field. Our main result is a homotopy invariance theorem for these groups.

Article
Kolesnikov A., Banakh T., Bogachev V. Functional Analysis and Its Applications. 2004. P. 23-47.
Article
Ilina A., Krichever I. M. Functional Analysis and Its Applications. 2017. Vol. 51. No. 1. P. 48-65.

New reductions of the 2D Toda equations associated with lower-triangular difference operators are proposed. Their explicit Hamiltonian description is obtained.

Article
Finkelberg M. V., Kubrak D. Functional Analysis and Its Applications. 2015. Vol. 49. No. 2. P. 135-141.

We slightly extend results of Evens and Mirković and “compute” the characteristic cycles of intersection cohomology sheaves on transversal slices in a double affine Grassmannian. We propose a conjecture relating the hyperbolic stalks and microlocalization at a torus-fixed point in a Poisson variety. © 2015, Springer Science+Business Media New York.

Article
В. В. Лебедев Функциональный анализ и его приложения. 2012. Т. 46. № 2. С. 52-65.

We obtain a partial solution of the problem on the growth of the norms of exponential functions with a continuous phase in the Wiener algebra. The problem was posed by J.-P. Kahane at the International Congress of Mathematicians in Stockholm in 1962. He conjectured that (for a nonlinear phase) one can not achieve the growth slower than the logarithm of the frequency. Though the conjecture is still not confirmed, the author obtained first nontrivial results.

Article
Бухштабер В.М., Тертычный С. И. Функциональный анализ и его приложения. 2016. Т. 50. № 3. С. 12-33.

Two new linear operators determining automorphisms of the solution space of a special double-confluent Heun equation in the general case are obtained. This equation has two singular points, both of which are irregular. The obtained result is applied to solve the nonlinear equation of the resistively shunted junction model for an overdamped Josephson junction in superconductors. The new operators are explicitly expressed in terms of structural polynomials, for which recursive computational algorithms are constructed. Two functional equations for the solutions of the special double-confluent Heun equation are found.

Article
Фейгин Б. Л. Функциональный анализ и его приложения. 1985. Т. 19. № 2. С. 52-62.
Article
Посицельский Л. Е. Функциональный анализ и его приложения. 2012. Т. 46. № 3. С. 71-80.

We prove that the algebra of closed differential forms on an (algebraic, formal, or analytic) disk with logarithmic singularities along several coordinate hyperplanes is Koszul (both nontopologically and topologically). A relation to variations of mixed Hodge-Tate structures is discussed in the introduction.

Article
Нетай И. В. Функциональный анализ и его приложения. 2013. Т. 47. № 3. С. 54-74.

We describe the syzygy spaces for the Segre embedding~$\bbP(U)\times\bbP(V)\subset\bbP(U\otimes V)$ in terms of representations of $\GL(U)\times \GL(V)$ and construct the minimal resolutions of the sheaves~$\mathscr{O}_{\bbP(U)\times\bbP(V)}(a,b)$ in~$D(\bbP(U\otimes V))$ for~$a\geqslant-\dim(U)$ and~$b\geqslant-\dim(V)$. Also we prove some property of multiplication on syzygy spaces of the Segre embedding.

Article
Кочетков Ю. Ю. Функциональный анализ и его приложения. 2002. Т. 36. № 3. С. 83-87.

Some special polynomial systems (antivandermond systems) and definition fields of their solutions are studied. In the case of four variables it is proved that definition field is an extension of degree 12 of real quadratic field.

Article
Ольшанский Г. И. Функциональный анализ и его приложения. 2016. Т. 49. № 4. С. 61-75.
Article
Шур М. Г. Функциональный анализ и его приложения. 1993. Т. 27. № 1. С. 92-93.
Article
Бухштабер В.М., Михайлов А. В. Функциональный анализ и его приложения. 2017. Т. 51. № 1. С. 4-27.
Article
Фейгин Е. Б. Функциональный анализ и его приложения. 2008. Т. 42. № 1. С. 63-77.
Article
Рыбников Г. Л. Функциональный анализ и его приложения. 1992. Т. 26. № 4. С. 75-77.
Article
Кричевер И. М. Функциональный анализ и его приложения. 2012. Т. 46. № 2. С. 37-51.

Using meromorphic differentials with real periods, we prove Arbarello's conjecture that any compact complex cycle of dimension g−n in the moduli space M_g of smooth algebraic curves of genus g must intersect the locus of curves having a Weierstrass point of order at most n.

Article
Р.С. Авдеев, Горфинкель Н. Е. Функциональный анализ и его приложения. 2012. Т. 46. № 3. С. 1-15.

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of representations of G on spaces of regular sections of homogeneous line bundles over G/H.