Functional Analysis and Its Applications最新文献

Given a semitopological semigroup (S), let (operatorname{WAP}(S)) and (operatorname{AP}(S)) be the algebras of weakly and strongly almost periodic functions on (S), respectively. This paper centers around the study of the fixed point property ((mathbf{F}_{*,s})): whenever (picolon Stimes K to K) is a jointly (*)-weak continuous nonexpansive action on a non-empty norm separable (*)-weak compact convex set (K) in the dual (E^*) of a Banach space (E), then there is a common fixed point for (S) in (K). We are primarily interested in answering the following problems posed by Lau and Zhang. (1) Let (S) be a discrete semigroup. If the fixed point property ((mathbf{F}_{*,s})) holds, does (operatorname{WAP}(S)) have a left invariant mean? (2) Is the existence of a left invariant mean on (operatorname{WAP}(S)) a sufficient condition to ensure the fixed point property ((mathbf{F}_{*,s}))? (3) Do the bicyclic semigroups (S_2=langle e,a,b,c colon ab=ac=erangle) and (S_3=langle e,a,b,c,d colon ac=bd=erangle) have the fixed point property ((mathbf{F}_{*,s}))? Among other things, characterization theorems of the amenability property of the algebras (operatorname{WAP}(S)) and (operatorname{AP}(S)) are also given.

The paper discusses an applicability condition of a cutoff regularization to a fundamental solution of the Laplace operator in the coordinate representation in the Euclidean space of dimension greater than two. To regularize, we consider a deformation of the solution in a sufficiently small ball centered at the origin by cutting off a singular component, and further supplementing it with a continuous function. It is shown that a set of functions satisfying the applicability condition is not empty. As an example, a family of functions is constructed that can be represented by applying a set of averaging operators to the non-regularized solution, and some specific examples are given. Additionally, it is demonstrated that there exist functions that satisfy the condition in a more strict formulation.

Meromorphic differentials on Riemann surfaces are said to be real-normalized if all their periods are real. Moduli spaces of real-normalized differentials on Riemann surfaces of given genus with prescribed orders of their poles and residues admit a stratification by the orders of zeroes of the differentials. Subsets of real-normalized differentials with a fixed polarized module of periods compose isoperiodic subspaces, which also admit this stratification. In this work, we prove connectedness of the principal stratum for the isoperiodic subspaces in the space of real-normalized differentials with a single pole of order two when all the periods are incommesurable.

Let (X) be a smooth toric variety defined by the fan (Sigma). We consider (Sigma) as a finite set with topology and define a natural sheaf of graded algebras (mathcal{A}_Sigma) on (Sigma). The category of modules over (mathcal{A}_Sigma) is studied (together with other related categories). This leads to a certain combinatorial Koszul duality equivalence.

We describe the equivariant category of coherent sheaves (mathrm{coh}_{X,T}) and a related (slightly bigger) equivariant category (mathcal{O}_{X,T}text{-}mathrm{mod}) in terms of sheaves of modules over the sheaf of algebras (mathcal{A}_Sigma). Eventually (for a complete (X)), the combinatorial Koszul duality is interpreted in terms of the Serre functor on (D^b(mathrm{coh}_{X,T})).

We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of (Nge 2) unidirectionally coupled maps of the two-dimensional torus (mathbb{T}^2), each of which is of Arnold’s cat map type. We provide sufficient conditions (independent of (N)) under which the chain gives rise to an Anosov diffeomorphism of (mathbb{T}^{2N}) for any (Nge 2).

In this paper, we investigate the spectrum of the differential operator (T) generated by an ordinary differential expression of order (n) with (mathrm{PT})-symmertic periodic (mtimes m) matrix coefficients. We prove that if (m) and (n) are odd numbers, then the spectrum of (T) contains all the real line. Note that in standard quantum theory, observable systems must be Hermitian operators, so as to ensure that the spectrum is real. Research on (mathrm{PT})-symmetric quantum theory is based on the observation that the spectrum of a (mathrm{PT})-symmetric non-self-adjoint operator can contain real numbers. In this paper, we discover a large class of (mathrm{PT})-symmetric operators whose spectrum contains all real axes. Moreover, the proof is very short.

New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and that the resulting DG algebras are smooth. This description allows us to show that some of these DG algebras determine smooth proper noncommutative curves that provide smooth minimal noncommutative resolutions for singular rational curves.

We give a description of finite-zone (mathcal{PT})-potentials in terms of explicit theta-functional formulas.

Generalizations of the theorems of Eberlein and Grothendieck on the precompactness of subsets of function spaces are considered: if (X) is a countably compact space and (C_p(X)) is a space of continuous functions on (X) in the topology of pointwise convergence, then any countably compact subspace of the space (C_p(X)) is precompact, that is, it has a compact closure. The paper provides an overview of the results on this topic. It is proved that if a pseudocompact (X) contains a dense Lindelöf (Sigma)-space, then pseudocompact subspaces of the space (C_p(X)) are precompact. If (X) is the product Čech complete spaces, then bounded subsets of the space (C_p(X)) are precompact. Results on the continuity of separately continuous functions are also obtained.

The Poincare construction in CR geometry allows us to estimate the dimension of the stabilizer in the Lie algebra of infinitesimal holomorphic automorphisms of the germ of a CR manifold by the dimension of the stabilizer in the corresponding algebra of the model surface of this germ. We give a negative answer to the following natural question: is there an algebraic Poincare construction, i.e., is it true that the stabilizer in the Lie algebra of automorphisms of the germ of a CR manifold is isomorphic to a Lie subalgebra of the stabilizer in the algebra of its model surface? We also give a negative answer to the corresponding question for the whole automorphisms algebra.