Table of contents

The equation is considered, where the operator in the region is representable in the form ; here has order , real coefficients in , contains derivatives in the variables , , and is elliptic in these variables, and for any real vector the equation , , for any real not proportional to does not have double real zeros . Bibliography: 3 references.

A Lie group is said to be effective if it is connected and contains no compact normal divisors. A factorization of a connected Lie group into the product of two connected subgroups, the first of which is maximally compact and the second completely solvable is called a polar factorization. In this article the following theorem is proved. Theorem.Any two polar factorizations of an effective Lie group are conjugate under an inner automorphism. Bibliography: 5 items.

The paper is concerned with problems of the form A(x,∂/∂x,p)u(x) = f(x) in G, B(x,∂/∂x,p)u(x) = g(x) on Γ. Here G is a region in Rⁿ_x with smooth boundary Γ; A and B are matrices of linear partial differential operators with smooth coefficients, depending polynomially on the complex parameter p. The operator A is obtained by replacing ∂/∂x by p in the operator A(x,∂/∂x, ∂/∂t), which is strongly hyperbolic in the sense of I. G. Petrovskiĭ. Under some supplementary assumptions, the existence and uniqueness of a strong solution in the spaces H_qs is demonstrated, and an a priori estimate in norms involving the parameter p is obtained for large values of Re p. Bibliography: 30 references.

This paper gives a construction leading to Deheuvels homology of compact metric spaces with coefficients in copresheaves of abelian groups. We construct an epimorphic map of Deheuvels homology onto Aleksandrov–Čech homology, whose kernel is expressed in terms of the derived functors of the inverse limit functor. We consider projective objects in the category of copresheaves of abelian groups and homology with coefficients in projective copresheaves. The fundamental result of the paper is the theorem that the Deheuvels homology of compact metric spaces with coefficients in copresheaves of abelian groups is a universal extension of Aleksandrov–Čech homology among homologies which satisfy the exactness condition and other natural requirements. Bibliography: 5 items.

This paper provides a systematic presentation of the connection between the theory of one-dimensional formal groups and the theory of unitary cobordism. Two new algebraic concepts are introduced: formal power systems and two-valued formal groups. A presentation of the general theory of formal power systems is given, and it is shown that cobordism theory gives a nontrivial example of a system which is not a formal group. A two-valued formal group is constructed whose ring of coefficients is closely related to the bordism ring of a symplectic manifold. Finally, applications of formal groups and power systems are made to the theory of fixed points of periodic transformations of quasicomplex manifolds. Bibliography: 17 citations

In this paper we study several extension problems for maps into spheres, and as a consequence we solve a problem by P. S. Aleksandrov on bicompact condensation. Furthermore, we define a new class of infinite-dimensional spaces, and in investigating them we generalize a classical result of Uryson on Cantor manifolds. Bibliography: 15 items.

An expanded presentation of results previously announced by the author (see MR 38 #1557) with a generalization to the case of an infinite-dimensional perturbation; continued. See MR 41 #7474 for the first part. Bibliography: 12 items.