Functional Analysis and Its Applications最新文献

There are many papers on the classification of singularities that are invariant or equivariant under the action of a finite group. However, since the problem is difficult, most of these papers consider only special cases, for example, the case of the action of a particular group of small order. In this paper, an attempt is made to prove general statements about equivariantly simple singularities; namely, singularities equivariantly simple with respect to irreducible actions of finite groups are classified. A criterion for the existence of such equivariantly simple singularities is also given.

The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used.

Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of distributions in (mathcal{S}_{0}'(mathbb{R})) in terms of their Stockwell transforms are obtained. An Abelian-type result relating the quasiasymptotic boundedness of Lizorkin distributions to the asymptotic behavior of their Stockwell transforms is given. Several asymptotic results for the distributional wavelet transform are also presented.

We derive various lower bounds for the numerical radius (w(A)) of a bounded linear operator (A) defined on a complex Hilbert space, which improve the existing inequality (w^2(A)geq frac{1}{4}|A^*A+AA^*|). In particular, for (rgeq 1), we show that

We give an “integration by parts” approach to Davies’ Hardy inequality. An improvement with a strictly larger Hardy weight is thereby obtained.

As is known, for isolated hypersurface singularities and complete intersections of positive dimension, the Milnor number is the least upper bound for the Tjurina number, i.e., (tau leqslant mu). In this paper we show that, for zero-dimensional complete intersections, the reverse inequality holds. The proof is based on properties of faithful modules over an Artinian local ring. We also exploit simple properties of the annihilator and the socle of the modules of Kähler differentials and derivations and the theory of duality in the cotangent complex of zero-dimensional singularities.

Bloch solutions of the difference Schrödinger equation with periodic complex potential on the real line are discussed. The case where the spectral parameter is outside the spectrum of the corresponding Schrödinger operator is considered.

The image of the Bethe subalgebra (B(C)) in the tensor product of representations of the Yangian (Y(mathfrak{gl}_n)) contains the full set of Hamiltonians of the Heisenberg magnet chain XXX. The main problem in the XXX integrable system is the diagonalization of the operators by which the elements of Bethe subalgebras act on the corresponding representations of the Yangian. The standard approach is the Bethe ansatz. As the first step toward solving this problem, we want to show that the eigenvalues of these operators have multiplicity 1. In this work we obtained several new results on the simplicity of spectra of Bethe subalgebras in Kirillov–Reshetikhin modules in the case of (Y(mathfrak{g})), where (mathfrak{g}) is a simple Lie algebra.

We describe one-dimensional central measures on numberings (tableaux) of ideals of partially ordered sets (posets). As the main example, we study the poset (mathbb{Z}_+^d) and the graph of its finite ideals, multidimensional Young tableaux; for (d=2), this is the ordinary Young graph. The central measures are stratified by dimension; in the paper we give a complete description of the one-dimensional stratum and prove that every ergodic central measure is uniquely determined by its frequencies. The suggested method, in particular, gives the first purely combinatorial proof of E. Thoma’s theorem for one-dimensional central measures different from the Plancherel measure (which is of dimension (2)).

Three intermediate class of spaces (mathscr{R}_1subset mathscr{R}_2subset mathscr{R}_3) between the classes of (F)- and (betaomega)-spaces are considered. The (mathscr{R}_1)- and (mathscr{R}_3)-spaces are characterized in terms of the extension of functions. It is proved that the classes of (mathscr{R}_1)-, (mathscr{R}_2)-, (mathscr{R}_3)-, and (betaomega)-spaces are not preserved by the Stone–Čech compactification.