Conjugacy problem in an automorphism group of an infinite tree

An algorithm recognizing the conjugacy of elements in the Grigorchuk 2-group is constructed.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 592–597, October, 1998.     

Asymptotic estimates for the approximation and entropy numbers of a one-weight Riemann-Liouville operator

We obtain two-sided estimates for the asymptotic behavior of the approximation and entropy numbers of a one-weight Riemann-Liouville operator of an arbitrary integer order acting in Lebesgue spaces on the semiaxis.     

The complete isomorphism class of an operator space

Suppose is an infinite-dimensional operator space and is a positive integer. We prove that for every there exists an operator space such that the formal identity map is a complete isomorphism, is an isometry, and . This provides a non-commutative counterpart to a recent result of W. Johnson and E. Odell.

     

Differential invariants of the transformation group of a homogeneous space

We demonstrate that the invariant operators on a homogeneous space generate differential invariants and invariant differentiation operators. The coordinate-free method of this article makes it possible to simply the computations essentially, namely to reduce them to operations of linear algebra. Some examples are exhibited.     

The HeatKernel ofthe Sym m etric Space P_n

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Embedding of Sobolev space in Orlicz space for a domain with irregular boundary

In this paper, we establish the embedding of a weighted Sobolev space in an Orlicz space for a domain with irregular boundary. We find an estimate of the order of growth of the N-function (defining the Orlicz space) and show that, under certain additional constraints on the weights, this estimate is sharp. We also establish the embedding in the space of continuous functions.     

The bicompletion of an asymmetric normed linear space

A biBanach space is an asymmetric normed linear space (X,‖·‖) such that the normed linear space (X,‖·‖^s) is a Banach space, where ‖x‖^s= max {‖x‖,‖-x‖} for all x∈X. We prove that each asymmetric normed linear space (X,‖·‖) is isometrically isomorphic to a dense subspace of a biBanach space (Y,‖·‖_Y). Furthermore the space (Y,‖·‖_Y) is unique (up to isometric isomorphism). This revised version was published online in August 2006 with corrections to the Cover Date.     

On hyperinvariant subspaces of contraction operators on a Banach space whose spectrum contains the unit circle

In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace. This research is supported by the Natural Science Foundation of P. R. China (No. 10771039)     

Solvability of Boundary Value Problems for Operator-Differential Equations of Mixed Type: The Degenerate Case

We obtain some results on solvability of boundary value problems for the equation B u _t –L u =f (t(0,)), where B and L are selfadjoint and dissipative operators defined in a Hilbert space E. The kernel of B may be nontrivial and L is uniformly dissipative on a subspace M of finite codimension.     

Norm of a multilinear integral operator from product of weighted-type spaces to weighted-type space

We investigate the following multilinear integral operator $$T_K^m(\overrightarrow{f})(x)={\int }_0^{\infty }\dots {\int }_0^{\infty }K(x,t_1,\dots ,t_m){\displaystyle \prod _{j=1}^m}{f}_j(t_j)d{t}_1\dots d{t}_m,$$ where $m\in ?$ and $K:{?}_{+}^{m+1}\to {?}_{+}$ is a continuous kernel function satisfying the condition $$K(x,g_1(x)s_1,\dots ,g_m(x)s_m)=h(x)K(1,s_1,\dots ,s_m),$$ for some functions $g_j,j=\stackrel{￣}{1,m}$, which are continuous, increasing, $g_j({?}_{+})={?}_{+},j=\stackrel{￣}{1,m}$, and a function $h:{?}_{+}\to {?}_{+}$, from a product of weighted-type spaces to weighted-type spaces of real functions. We calculate the norm of the operator, extending and complementing some results in the literature. We also give an explanation for a relation between integrals of an L^p integrable function and its radialization on ${?}^n$.     

On the variation of a metric and its application

Some of the variation formulas of a metric were derived in the literatures by using the local coordinates system, In this paper, We give the first and the second variation formulas of the Riemannian curvature tensor, Ricci curvature tensor and scalar curvature of a metric by using the moving frame method. We establish a relation between the variation of the volume of a metric and that of a submanifold. We find that the latter is a consequence of the former. Finally we give an application of these formulas to the variations of heat invariants. We prove that a conformally flat metric g is a critical point of the third heat invariant functional for a compact 4-dimensional manifold M, then （M, g） is either scalar flat or a space form.     

Lamperti-type operators on a weighted space of continuous functions

For a locally convex Hausdorff topological vector space and for a system of weights vanishing at infinity on a locally compact Hausdorff space , let be the weighted space of -valued continuous functions on with the locally convex topology derived from the seminorms which are weighted analogues of the supremum norm. A characterization of the orthogonality preserving (Lamperti-type) operators on is presented in this paper.

     

Approximation of the functions in weighted Lebesgue spaces with variable exponent

In the present work, we investigate the approximation problems of the functions by Fejér, and Zygmund means of Fourier trigonometric series in weighted Lebesgue spaces with variable exponents and of the functions by Fejér and Abel–Poisson sums of Faber series in weighted Smirnov classes with variable exponents defined on simply connected domains with a Dini-smooth boundary of the complex plane.     

Spectral Analysis of Certain Self-Adjoint Differential Operators in a Space with Indefinite Metric

A second-order differential operator self-adjoint with respect to an indefinite metric on the circle is considered. The spectral resolution of this operator is found. The hypergeometric function is used in the computation of the Plancherel measure.     

On a Class of Analytic Operator Functions and Their Linearizations

We consider an operator function T in a Krein space which can formally be written as (0.1)but the last term on the right of (0.1) is replaced by a relatively form‐compact perturbation of a similar form. We study relations between the operator function T, a selfadjoint operator M in some Krein space, associated with T, and an operator which can be constructed with the help of the operator function –T^–1. The results are applied to a Sturm‐Liouville problem with a coefficient depending rationally on the eigenvalue parameter.     

Well-Definedness of the Cauchy Problem for the One-Dimensional Equations of Viscous Heat Conducting Gas with Initial Data from Lebesgue Spaces

Mathematical Notes -     

The topological structure of a certain Menger space

In this paper we will reconsider the topological structure of Menger probabilistic normed spaces (briefly PN-spaces) under the t-norm M. We will prove that this topology is compatible with the topology induced by a countable and separating family of semi-norms, and hence the well-known theorems of classical functional analysis (such as the principle of uniform boundedness, open mapping and closed graph theorems) are valid in this context also. We will meanwhile obtain a method by which one may construct easily a large class of PN-spaces. Finally, using this method, we see that a certain subspace of bounded linear operators between PN-spaces, i.e. the class of strongly bounded linear operators, has a natural PN structure.     

The Fine Spectra of the Difference Operator △ Over the Sequence Space bvp, （1 ≤ p 〈 ∞）^＊

The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg＇s classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.