Functional Analysis and Its Applications最新文献

The superposition principle delivers a probabilistic representation of a solution ({mu_t}_{tin[0, T]}) of the Fokker–Planck–Kolmogorov equation (partial_tmu_t=L^{*}mu_t) in terms of a solution (P) of the martingale problem with operator (L). We generalize the superposition principle to the case of equations on a domain, examine the transformation of the measure (P) and the operator (L) under a change of variables, and obtain new conditions for the validity of the superposition principle under the assumption of the existence of a Lyapunov function for the unbounded part of the drift coefficient.

For elliptic divergent self-adjoint second-order operators with (varepsilon)-periodic measurable coefficients acting on the whole space (mathbb{R}^d), resolvent approximations in the operator norm (|!,boldsymbolcdot,!|_{H^1to H^1}) with remainder of order (varepsilon^2) as (varepsilonto 0) are found by the method of two-scale expansions with the use of smoothing.

We prove a restricted inverse prime number theorem for an arithmetical semigroup with polynomial growth of the abstract prime counting function. The adjective “restricted” refers to the fact that we consider the counting function of abstract integers of degree (le t) whose prime factorization may only contain the first (k) abstract primes (arranged in nondescending order of their degree). The theorem provides the asymptotics of this counting function as (t,ktoinfty). The study of the discussed asymptotics is motivated by two possible applications in mathematical physics: the calculation of the entropy of generalizations of the Bose gas and the study of the statistics of propagation of narrow wave packets on metric graphs.

Extensions of finite-dimensional nilpotent Lie algebras, in particular, solvable extensions, are considered. Some properties of maximal extensions are proved. A counterexample to L. Šnobl’s conjecture concerning the uniqueness of maximal solvable extensions is constructed.

Unitary flows (T_t) of dynamical origin such that, for any countable (Qsubset (0,+infty)), the spectrum of the tensor product (bigotimes_{qin Q} T_q ) is simple are constructed. All typical flows preserving a sigma-finite measure have this property.

Let (Omegasubsetmathbb{R}^n) be a bounded domain with smooth boundary (partialOmega), let (D(x)in C^infty(overlineOmega)) be a defining function of the boundary, and let (B(x)in C^infty(overlineOmega)) be an (ntimes n) matrix function with self-adjoint positive definite values (B(x )=B^*(x)>0) for all (xinoverlineOmega) The Friedrichs extension of the minimal operator given by the differential expression (mathcal{A}_0=-langlenabla,D(x )B(x)nablarangle) to (C_0^infty(Omega)) is described.

Approximations of the image and integral funnel of a closed ball of the space (L_p), (p>1), under a Urysohn-type integral operator are considered. A closed ball of the space (L_p), (p>1), is replaced by a set consisting of a finite number of piecewise constant functions, and it is proved that, for appropriate discretization parameters, the images of these piecewise constant functions form an internal approximation of the image of the closed ball. This result is applied to approximate the integral funnel of a closed ball of the space (L_p), (p>1), under a Urysohn-type integral operator by a set consisting of a finite number of points.

We study semifinite harmonic functions on the zigzag graph, which corresponds to the Pieri rule for the fundamental quasisymmetric functions ({F_{lambda}}). The main problem, which we solve here, is to classify the indecomposable semifinite harmonic functions on this graph. We show that these functions are in a natural bijective correspondence with some combinatorial data, the so-called semifinite zigzag growth models. Furthermore, we describe an explicit construction that produces a semifinite indecomposable harmonic function from every semifinite zigzag growth model. We also establish a semifinite analogue of the Vershik–Kerov ring theorem.

In this paper, the property (UWE) and the a-Weyl theorem for bounded linear operators are studied in terms of the property of topological uniform descent. Sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space to have the property (UWE) and satisfy the a-Weyl theorem are established. In addition, new criteria for the fulfillment of the property (UWE) and the a-Weyl theorem for an operator function are discussed. As a consequence of the main theorem, results on the stability of the property (UWE) and the a-Weyl theorem are obtained.

Cyclic vectors and proper closed invariant subspaces of the backward shift operator in the Schwartz modules of entire functions of exponential type are described. The results are applied to describe ideals of the algebra of infinitely differentiable functions on a closed or open interval containing (0) with Duhamel product as multiplication.