Carleson measures and the heat equation

Let { }, where { } is the open unit disk on the complex plane { }. In G, we consider analytic solutions u(t, z) ({ }, { }) of the heat equation 2u_t=u_zz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have { } Bibliography: 17 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155. Translated by S. V. Kislyakov.     

Invariant and quasi-invariant transformations of measures that correspond to stable processes with independent increments

Let ξ(t), t ∈ [0, 1], be a strictly stable process with an index of stability α ∈ (0, 2). By we denote the law of ξ in the Skorokhod space [0,1]. For arbitrary strictly stable process ξ, we construct a semigroup of transformations of [0, 1] for which the measure is quasi-invariant. For strictly stable processes with positive and negative jumps, we construct a group of transformations of [0, 1] for which the measure is quasi-invariant. In the symmetric case, this group is a group of invariant transformations. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 135–149.     

On the range of a generalized derivation

A generalized derivation , is defined by the formula , where and is the Banach algebra of bounded linear operators in a Hilbert space . Sufficient conditions under which and are given. Bibliography: 8 titles. Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 111–119.     

Transformation of measures generated by jump Lévy processes

Let ξ(t), t ∈ [0, 1], be a jump Lévy process. We denote by the law of ξ in the Skorokhod space [0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of -preserving transformations of the space [0, 1]. Bibliography: 11 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 175–188.     

A local duality theorem for categories of modules

Let Λ be an associative ring with identity and let be the category of left unitary Λ-modules. A subcateqory of the category is said to be small if the pairwise nonisomorphic objects of form a set. The main result of this paper consists of the fact that for every small full subcategory , there exists a ring Γ such that is dual to a small full subcategory of the category . Some applications of this result are indicated. Bibliography: 3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73.     

Invariants of classCk for finite coxeter groups and their representations in terms of anisotropic spaces

This article is devoted to the study of representations of C^k { } functions f invariant with respect to finite Coxeter groups W in the form f=F op, where p is a base in the algebra of W-invariant polynomials. We examine the lowering of smoothness of F as compared with f and conclude that this lowering has an anisotropic nature and that, more precisely, at each point Po it is described by a vector { }. We examine the cases W=A_n, B_n, D_n, { }; in each case the greatest component { } of { } is equal to the Coxeter number of the stabilizer W_yo of the point yo, where po=p(yo). Bibliography: 22 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 46–70. Translated by S. Yu. Pilyugin.     

Sui fibrati con struttura quaternionale generalizzata

Summary Quaternion generalized fiber bundles are studied, both isomorphic to global tensorial product ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a splitting principle are proved for bundles . On this ground and founding on a convenient bundle B_E → X associated to jaz (that we call Bonan's bundle and for which ɛ( =ɛ(B_E)) relations are stated among Stiefel-Whitney classes of , B_E and the class ɛ.

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Entrata in Redazione il 14 agosto 1974.

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Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni.     

A question in the theory of saturated formations of finite soluble groups

This paper examines the following question. If and are saturated formations then is defined to be the class of all soluble groups whose belong to . In general is a formation, but need not be a saturated formation. Here the smallest saturated formation containing is studied.     

Lacunary series and pseudocontinuations

The main goal of this paper is to prove the following statement. Let be a function holomorphic and of bounded characteristic in the unit disk , where E is a Λ(1)-subset of ℤ₊. Assume that f has a pseudocontinuation of bounded characteristic to the annulus {zɛℂ:1<|z|<R}. Then f admits analytic continuation to the disk R . In particular, f is a polynomial if R=+∞. Bibliography: 16 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 16–32. Translated by A. B. Aleksandrov.     

Spectral synthesis in spaces invariant under composition semigroups

If φt is a continuously differentiable composition semigroup of analytic endomorphisms of the disk , then all closed subspaces of Hol( ) invariant with respect to this semigroup (acting by compositions) admit spectral synthesis. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 206, 1993, pp. 55–77. Translated by V. I. Vasyunin.     

Pseudo algebraically closed fields over rings

We prove that for almost allσ ∈G ℚ the field has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→ there exists a point a ∈ such thatϕ(a) ∈ ℤ^r. We then say that is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ.     

Baer cotorsion Pairs

LetR be a unital associative ring and two classes of leftR-modules. In [St3] the notion of a ( ) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses is called a ( ) pair if it is maximal with respect to the classes and the condition Ext _R ¹ (V, W)=0 for all . In this paper we study pairs whereR = ℤ and is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every pair is singly cognerated underV=L. The author was supported by a DFG grant.     

The theory of multi-dimensional polynomial approximation

We consider the problem of polynomial approximation to a real valued functionf defined on a compact set . An approximation theorem is proven in terms of the newly defined modulus of approximation. It is shown to imply a multidimensional Jackson type theorem which is stronger than previously known results even for the interval [−1, 1]. A strong multidimensional Bernstein type inverse theorem is also proven. We allow quite general approximation quasi-norms including for 0<q≤∞. We have found that the space of polynomials ℙ on a compact setX induces a semimetric which encapsulates the local structure of ℙ. Any semimetric ρ equivalent to suffices for the rough theory presented here. Many examples of sets and their metrics are presented.     

Topological and metric product\mathbb{Z}^d -actions and their applications-actions and their applications

We show that for a -action Ψ being the Kronecker sum of a symbolic strictly ergodic -actionT and a Chacon -actionS, the rank (covering number) of Ψ is the same as that forT. Using this result we construct, for a given natural numberr≥2 and a real numberb∈(0,1) withr\b≥1, a -action with rankr, covering numberb and a simple spectrum. On the other hand, for any positive integersr, m with 1≤m≤r≤∞ we construct a -action with rankr and spectral multiplicitym.     

Measure-valued almost periodic functions

We consider Stepanov almost periodic functions μ ∈ ranging in the metric space of Borel probability measures on a complete separable metric space is equipped with the Prokhorov metric). The main result is as follows: a function , belongs to if and only if for each bounded continuous function , the function is Stepanov almost periodic (of order 1) and

Factorizations of composition formations

It is proved that, if is a singly generated composition formation, where , then is a composition formation. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 389–395, March, 1999.     

Categories with homotopy determine a closed model structure

In a category with homotopy (Definition 1.1), one can define a natural concept of (co)fibrations and weak equivalences (Sec. 2) such that some properties of a closed model category hold. If is a complete and cocomplete category (with respect to finite limits) with simplicial homotopy (Definition 1.3), one achieves a full closed model structure in (Theorem 4.6). For each category with homotopy , there exists a category with simplicial homotopy (see Sec. 5) (the simplicial envelope of ). If is already a complete category with simplicial homotopy, then is Quillen equivalent to (Theorem 5.9). __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 41, Topology and Its Applications, 2006.     

Protuberance effect in the generalized functional Strassen-Révész law

The set of increments of the Wiener process