Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Том 53, № 1 (2019)
- Жылы: 2019
- Мақалалар: 10
- URL: https://journals.rcsi.science/0016-2663/issue/view/14594
Article
Evgenii Alekseevich Gorin
1-2
Directional Short-Time Fourier Transform and Quasiasymptotics of Distributions
Аннотация
We give an Abelian type result relating the quasiasymptotic boundedness of tempered distributions to the asymptotics of their directional short-time Fourier transform (DSTFT). We also prove several Abelian-Tauberian results characterizing the quasiasymptotic behavior of distributions in \(\mathscr{S}'\)(ℝn) in terms of their DSTFT with fixed direction.
3-10
Degrees of Cohomology Classes of Multisingularities in Hurwitz Spaces of Rational Functions
Аннотация
Hurwitz spaces are spaces of meromorphic functions with prescribed orders of poles on curves of a given genus. In this article, we derive new formulas for the degrees of the strata of Hurwitz spaces of genus 0 corresponding to functions that have two degenerate critical values with prescribed partitions of multiplicities of the preimages. More precisely, one of the critical values has an arbitrary multiplicity of the preimages, while the other is the simplest degenerate critical value.
11-22
Two-Dimensional Periodic Schrödinger Operators Integrable at an Energy Eigenlevel
Аннотация
The main goal of the first part of the paper is to show that the Fermi curve of a two-dimensional periodic Schrödinger operator with nonnegative potential whose points parameterize the Bloch solutions of the Schrödinger equation at the zero energy level is a smooth M-curve. Moreover, it is shown that the poles of the Bloch solutions are located on the fixed ovals of an antiholomorphic involution so that each but one oval contains precisely one pole. The topological type is stable until, at some value of the deformation parameter, the zero level becomes an eigenlevel for the Schrödinger operator on the space of (anti)periodic functions. The second part of the paper is devoted to the construction of such operators with the help of a generalization of the Novikov-Veselov construction.
23-36
Free Algebras of Hilbert Automorphic Forms
Аннотация
Let d > 0 be a square-free integer, and let Ld be the corresponding Hilbert lattice. Suppose given a finite-index subgroup Γ of O+(Ld) generated by reflections and containing -id and let A(Γ) be the algebra of Γ-automorphic forms. It is proved that if the algebra A(Γ) is free, then d ∈ {2, 3, 5, 6,13, 21}.
37-50
51-60
Brief Communications
On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space
Аннотация
The solvability of the equation A(x) = f(x) on the sphere of a Hilbert space and the dimension of its solution set are studied in the case where A is a closed surjective operator and f is an odd Lipschitz mapping. A kind of analogue of the infinite-dimensional version of the Borsuk-Ulam theorem is obtained.
61-64
65-68
On the Homogenization of the Stationary Periodic Maxwell System in a Bounded Domain
Аннотация
In a bounded domain \(\mathscr{O}\) ⊂ ℝ3 of class C1,1, the stationary Maxwell system with boundary conditions of perfect conductivity is considered. It is assumed that the dielectric permittivity and the magnetic permeability are given by η(x/ε) and μ(x/ε), where η and μ are symmetric bounded positive definite matrix-valued functions periodic with respect to some lattice in ℝ3. Here ε > 0 is a small parameter. It is known that, as ε > 0, the solutions of the Maxwell system weakly converge in L2(\(\mathscr{O}\)) to the solutions of the homogenized Maxwell system with constant effective coefficients. Classical results are improved and approximations for the solutions in the L2(\(\mathscr{O}\))-norm with error estimates of operator type are found.
69-73
On the Symmetrizations of ε-Isometries on Banach Spaces
Аннотация
A weak stability bound for the symmetrization Θ = (f(·) − f(−·))/2 of a general ε-isometry f from a Banach space X to a Banach space Y is presented. As a corollary, the following somewhat surprising weak stability result is obtained: For every x* ∈ X*, there exists ϕ ∈ Y* with ‖ϕ‖ = ‖x*‖ ≔ r such that \(\mid\langle{x}^*,x\rangle-\langle\varphi,\Theta(x)\rangle\mid\;\leqslant\frac{3}{2}r\varepsilon\;\;\;{\rm{for\;all}}\;x\in{X}.\)
This result is used to prove new stability theorems for the symmetrization Θ of f.
74-77