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In this paper a certain continuous family , , of finite covers by holomorphically complete domains is constructed for a compact complex space such that if then and for all and . It is proved that for each coherent sheaf over there exist positive constants and such that for any , with , if is a coboundary then one can find a cochain such that and

Bibliography: 4 items.

The principal result of the present work consists in the proof that an intersection of quadrics passing through a canonical curve is a reduced variety. The possible cases when the intersection of quadrics does not coincide with the curve itself are also examined in this article. Figures: 1. Bibliography: 8 references.

In this paper we prove the following Theorem. Let be a regular simply connected surface of class in . There exist positive absolute constants and such that if , where is the Gaussian curvature and is the area element on , the estimate holds. Bibliography: 11 items.

The main result established in this article is the following. Let be an arbitrary negative nonintegral number. Then every continuous function can be changed on a set of arbitrarily small measure so that if denotes the new function, then the sequence of the -means (corresponding to the method ) of the function contains a subsequence converging uniformly to the function . Bibliography: 3 items.

In this work there are investigated pseudodifferential operators of an infinite number of variables whose symbols, roughly speaking, are comparable with a fractional power of a fixed elliptic quadratic form. A composition formula for such operators is proved. Applications are made to the theory of elliptic and parabolic operators of higher orders. Figures: 2. Bibliography: 8 items.