Abstract:The explicit upper Bellman function is found for the natural dyadic maximal operator acting from into . As a consequence, it is shown that the norm of the natural operator equals for all , and so does the norm of the classical dyadic maximal operator. The main result is a partial consequence of a theorem for the so-called -trees, which generalize dyadic lattices. The Bellman function in this

Abstract:The classical Grauert and Ramspott theorems constitute the foundation of the Oka principle on Stein spaces. In this paper, similar results are established on the maximal ideal space of the Banach algebra  of bounded holomorphic functions on the open unit disk . The results are illustrated by some examples and applications to the theory of operator-valued functions.

Abstract:A complete series of trace formulas for the one-dimensional Stark operator on the entire axis with a rapidly decreasing potential is constructed. The Stark equation is related to the cylindrical Korteweg-de Vries equation by the pair (-). For this equation, infinite series of integrals of motion is constructed that corresponds to the trace formulas for the Stark operator.

Abstract:In the author's earlier paper [Revyakov M., J. Multivariate Anal. 116 (2013) 25-34] concerning mathematical statistics, a need arose to employ functions called ``Schur-convex functions of the 2nd order with respect to two variables''. In the present paper, the class of Schur-convex functions of the 2nd order in variables is introduced. Necessary and sufficient conditions (in the form of analogs

Abstract:Cylindrical acoustic waveguides with constant cross-section  are considered, specifically, a straight waveguide and a locally curved waveguide that depends on a parameter . For , in two different settings ( and ), the task is to find an eigenvalue that is embedded in the continuous spectrum of the waveguide and, hence, is inherently unstable. In other words, a solution of the Neumann problem

Abstract:The SRA-free condition for metric spaces (that is, spaces without Small Rough Angles) was introduced by Zolotov to study rectifiability for self-contracted curves in various metric spaces. A Möbius invariant version of this notion is introduced, which allows one to show that the zz-distance associated with the respective Möbius structure on the circle is nondegenerate. This result is an important

Abstract:A special version of the corona theorem in several variables, valid when all but one of the data functions are smooth, is used to generalize, to the polydisk and to the ball, the results obtained by El Fallah, Kellay, and Seip about the cyclicity of nonvanishing bounded holomorphic functions in sufficiently large Banach spaces of analytic functions determined either by weighted sums of powers

Abstract:The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth schemes over a field of characteristic different form two is proved. Namely, for any such sheaf , isomorphism is established, where is an essentially smooth local Henselian scheme with a separable residue field over . As a consequence, the rigidity theorem for the presheaves for any smooth

Abstract:We consider a third-order nonselfadjoint differential operator with square summable coefficients whose domain is defined by quasiperiodic boundary conditions. For this operator, using the method of similar operators, we obtain an asymptotic behavior of eigenvalues, estimates of the deviations of spectral projections, and the equiconvergence of spectral decompositions.

Abstract:Let be a semilocal Dedekind domain with fraction field . It is shown that two hereditary -orders in central simple -algebras that become isomorphic after tensoring with and with some faithfully flat étale -algebra are isomorphic. On the other hand, this fails for hereditary orders with involution. The latter stands in contrast to a result of the first two authors, who proved this statement

Abstract:This paper is devoted to almost subnormal subgroups of the general linear group of degree over a division ring that satisfy a generalized power central group identity.

Abstract:This is a continuation of the study of subgroups of the Chevalley group over a ring with root system and weight lattice that contain the elementary subgroup over a subring of . A. Bak and A. V. Stepanov considered recently the case of the symplectic group (simply connected group with root system ) in characteristic 2. In the current article, that result is extended to the case of and for the

Abstract:In , consider a selfadjoint matrix second order elliptic differential operator , . The principal part of the operator is given in a factorized form, the operator contains first and zero order terms. The operator is positive definite, its coefficients are periodic and depend on . The behavior in the small period limit is studied for the operator exponential , . The approximation in the -operator

Abstract:The paper is devoted to a noncommutative holomorphic functional calculus and its application to noncommutative algebraic geometry. A description is given for the noncommutative (infinite-dimensional) affine spaces , , , and for the projective spaces within Kapranov's model of noncommutative algebraic geometry based on the sheaf of formally-radical holomorphic functions of elements of a nilpotent