Functional Analysis and Its Applications最新文献

We study the global stability of polynomial stochastic operators on the probability simplex and analyze their contraction properties. A nonlinear analogue of the Perron–Frobenius theorem is established for some classes of polynomial stochastic operators. We also propose a novel Monte-Carlo method for stochastic hyper-matrices that guarantees the global stability of polynomial stochastic operators at any prescribed stochastic vector. Finally, we establish a nonlinear mean ergodic theorem for some classes of polynomial stochastic operators.

We show that on infinite-dimensional function spaces, there exist unbounded functionals that take at most one nonzero value on an arbitrary family of elements whose supports are pairwise disjoint.

We note that the canonical semi-orthogonal decompositions of the derived category of a poset scheme induce similar decompositions of the subcategory of perfect complexes.

Among central measures on the path space of the Young–Fibonacci lattice, the so-called Plancherel measure, whose ergodicity was proved by Kerov and Gnedin, plays a special role. The goal of this article is to prove the hypothesis of Kerov and Goodman that all other measures on the Martin boundary they described for this graph are also ergodic. The measures are parametrized by an infinite word of digits 1 and 2 and a positive parameter (betale1) (the case (beta=0) corresponds to the Plancherel measure). In this article, we prove the statements which correspond to the cases (beta=1) and (betain (0,1)).

We give several new examples of infinite-type interval translation maps which do not belong to any class of such maps previously described in the literature. All of our examples are self-similar. We prove that all of these examples are uniquely ergodic and weak mixing, and we also discuss possible generalizations of our constructions.

We prove a lower bound for the Milnor number of a function germ invariant with respect to a finite abelian group action. It is shown that this bound is tight for functions of arbitrarily many variables. We also prove that function germs which attain this lower bound are equivariantly stable, i.e., they are invariant analogues of Morse singularities.

We construct a continual family of pairwise disjoint Gaussian automorphisms whose even factors have the same Lebesgue spectrum.

In this paper, we find a maximal set of algebraically independent rational invariants of non-degenerate real model CR-quadrics of CR-type ((3, 3)). Using this, we construct holomorphic invariant differential forms on CR-manifolds.

In his paper (1973) Lance studied the notion of weak expectations in the setting of direct sums of representations of a (C^*)-algebra. The main purpose of this article is to extend this study to the framework of direct integrals. To achieve this, we introduce a special class of weak expectations for a representation of a separable, unital (C^*)-algebra called decomposable weak expectation. We give necessary and sufficient conditions for such kind of weak expectations to exist for a given representation. Then we define decomposable measures on the state space of a (C^*)-algebra and show that the GNS representation of a state admits a decomposable weak expectation if and only if there is a decomposable measure on the state space. The article concludes with an example of a decomposable weak expectation.

The work proves that, for finite three-dimensional upper-triangular groups over a field of odd characteristic generated by pseudoreflections, the maximal unipotent subgroup of which is abelian, the ring of invariants is polynomial if and only if the maximal unipotent subgroup is generated by pseudoreflections or does not contain transvections.